929.sagews

sage: [power_mod(n,11,5)for n in xrange(0, 61)] #A070471    n^3 mod 5.   A070690    n^7 mod 5.

[0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0]

sage: [power_mod(n,11,6)for n in xrange(0, 61)] #okA010875    Simple periodic sequence.

[0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0]

sage: [power_mod(n,5,7)for n in xrange(0, 101)] #okA070593   n^5 mod 7. Equivalently n^11 mod 7.

[0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4]

sage: [power_mod(n,11,7)for n in xrange(0, 101)] #okA070593   n^5 mod 7. Equivalently n^11 mod 7.

[0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4, 5, 2, 3, 6, 0, 1, 4]

sage: [power_mod(n,11,8)for n in xrange(0, 61)] #ok A109753   n^3 mod 8; the periodic sequence {0,1,0,3,0,5,0,7}.

[0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0]

sage: [power_mod(n,11,9)for n in xrange(0, 61)] #okA070595    n^5 mod 9.

[0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0]

sage: [power_mod(n,11,10)for n in xrange(0, 61)] #ok A008960  Final digits of cubes.

[0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0]

sage: [power_mod(n,11,11)for n in xrange(0, 78)] #A010880   Simple periodic sequence.

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0]

sage: [power_mod(n,11,12)for n in xrange(0, 78)] #ok A070474   n^3 mod 12.

[0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5]

sage: [power_mod(n,11,13)for n in xrange(0, 95)] #új n^11 mod 13.A167628 n^11 mod 13.

[0, 1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12, 0, 1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12, 0, 1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12, 0, 1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12, 0, 1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12, 0, 1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12, 0, 1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12, 0, 1, 7, 9]

sage: [power_mod(n,11,14)for n in xrange(0, 95)] #ok>>A070599   n^5 mod 14.

[0, 1, 4, 5, 2, 3, 6, 7, 8, 11, 12, 9, 10, 13, 0, 1, 4, 5, 2, 3, 6, 7, 8, 11, 12, 9, 10, 13, 0, 1, 4, 5, 2, 3, 6, 7, 8, 11, 12, 9, 10, 13, 0, 1, 4, 5, 2, 3, 6, 7, 8, 11, 12, 9, 10, 13, 0, 1, 4, 5, 2, 3, 6, 7, 8, 11, 12, 9, 10, 13, 0, 1, 4, 5, 2, 3, 6, 7, 8, 11, 12, 9, 10, 13, 0, 1, 4, 5, 2, 3, 6, 7, 8, 11, 12]

sage: [power_mod(n,11,16)for n in xrange(0, 95)] #okA167166  Z.L. n^7 mod 16.

[0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0]

sage: [power_mod(n,11,15)for n in xrange(0, 95)] #ok nem akarom A070477   n^3 mod 15. A070697   n^7 mod 15.

[0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4]

sage: [power_mod(n,11,17)for n in xrange(0, 95)] #nnnnnnnn

[0, 1, 8, 7, 13, 11, 5, 14, 2, 15, 3, 12, 6, 4, 10, 9, 16, 0, 1, 8, 7, 13, 11, 5, 14, 2, 15, 3, 12, 6, 4, 10, 9, 16, 0, 1, 8, 7, 13, 11, 5, 14, 2, 15, 3, 12, 6, 4, 10, 9, 16, 0, 1, 8, 7, 13, 11, 5, 14, 2, 15, 3, 12, 6, 4, 10, 9, 16, 0, 1, 8, 7, 13, 11, 5, 14, 2, 15, 3, 12, 6, 4, 10, 9, 16, 0, 1, 8, 7, 13, 11, 5, 14, 2, 15]

sage: [power_mod(n,11,18)for n in xrange(0, 95)] #ok>>A070602  n^5 mod 18.

[0, 1, 14, 9, 16, 11, 0, 13, 8, 9, 10, 5, 0, 7, 2, 9, 4, 17, 0, 1, 14, 9, 16, 11, 0, 13, 8, 9, 10, 5, 0, 7, 2, 9, 4, 17, 0, 1, 14, 9, 16, 11, 0, 13, 8, 9, 10, 5, 0, 7, 2, 9, 4, 17, 0, 1, 14, 9, 16, 11, 0, 13, 8, 9, 10, 5, 0, 7, 2, 9, 4, 17, 0, 1, 14, 9, 16, 11, 0, 13, 8, 9, 10, 5, 0, 7, 2, 9, 4, 17, 0, 1, 14, 9, 16]

sage: [power_mod(n,13,13)for n in xrange(0, 95)] #nnnnnnnnnn

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 1, 2, 3]

sage: [power_mod(n,13,14)for n in xrange(0, 95)] #ok>>A070696    n^7 mod 14.

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

sage: [power_mod(n,25,25)for n in xrange(0, 95)] #ok>>A070609   n^5 mod 25.

[0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24]

sage: [power_mod(n,11,118)for n in xrange(0, 61)] #nnnnnnn

[0, 1, 42, 29, 112, 79, 38, 35, 102, 15, 14, 77, 62, 55, 54, 49, 36, 27, 40, 25, 116, 71, 48, 31, 8, 105, 68, 81, 26, 7, 52, 33, 96, 109, 72, 51, 28, 11, 106, 61, 34, 19, 32, 23, 10, 5, 4, 115, 100, 45, 44, 75, 24, 21, 98, 65, 30, 17, 58, 59, 60]

sage: [power_mod(n,5,9)for n in xrange(0, 101)] #ok A070595  	  n^5 mod 9.

[0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1]

sage: [power_mod(n,5,10)for n in xrange(0, 81)] #A010879    Final digit of n.

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0]

sage: [power_mod(n,5,11)for n in xrange(0, 81)] #ok A070596  	  n^5 mod 11.

[0, 1, 10, 1, 1, 1, 10, 10, 10, 1, 10, 0, 1, 10, 1, 1, 1, 10, 10, 10, 1, 10, 0, 1, 10, 1, 1, 1, 10, 10, 10, 1, 10, 0, 1, 10, 1, 1, 1, 10, 10, 10, 1, 10, 0, 1, 10, 1, 1, 1, 10, 10, 10, 1, 10, 0, 1, 10, 1, 1, 1, 10, 10, 10, 1, 10, 0, 1, 10, 1, 1, 1, 10, 10, 10, 1, 10, 0, 1, 10, 1]

sage: [power_mod(n,5,12)for n in xrange(0, 81)] # ok A070597  	  n^5 mod 12.

sage: [power_mod(n,5,13)for n in xrange(0, 93)] # ok A070598  	 	 n^5 mod 13.

[0, 1, 6, 9, 10, 5, 2, 11, 8, 3, 4, 7, 12, 0, 1, 6, 9, 10, 5, 2, 11, 8, 3, 4, 7, 12, 0, 1, 6, 9, 10, 5, 2, 11, 8, 3, 4, 7, 12, 0, 1, 6, 9, 10, 5, 2, 11, 8, 3, 4, 7, 12, 0, 1, 6, 9, 10, 5, 2, 11, 8, 3, 4, 7, 12, 0, 1, 6, 9, 10, 5, 2, 11, 8, 3, 4, 7, 12, 0, 1, 6, 9, 10, 5, 2, 11, 8, 3, 4, 7, 12, 0, 1]

sage: [power_mod(n,5,14)for n in xrange(0, 93)] #okA070599  n^5 mod 14.

[0, 1, 4, 5, 2, 3, 6, 7, 8, 11, 12, 9, 10, 13, 0, 1, 4, 5, 2, 3, 6, 7, 8, 11, 12, 9, 10, 13, 0, 1, 4, 5, 2, 3, 6, 7, 8, 11, 12, 9, 10, 13, 0, 1, 4, 5, 2, 3, 6, 7, 8, 11, 12, 9, 10, 13, 0, 1, 4, 5, 2, 3, 6, 7, 8, 11, 12, 9, 10, 13, 0, 1, 4, 5, 2, 3, 6, 7, 8, 11, 12, 9, 10, 13, 0, 1, 4, 5, 2, 3, 6, 7, 8]

sage: [power_mod(n,5,15)for n in xrange(0, 89)] #ok új n^5 mod 15. A167463 n^5 mod 15.

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]

sage: [power_mod(n,5,16)for n in xrange(0, 89)] #ok új n^5 mod 16. A167465 n^5 mod 16.

[0, 1, 0, 3, 0, 5, 0, 7, 0, 9, 0, 11, 0, 13, 0, 15, 0, 1, 0, 3, 0, 5, 0, 7, 0, 9, 0, 11, 0, 13, 0, 15, 0, 1, 0, 3, 0, 5, 0, 7, 0, 9, 0, 11, 0, 13, 0, 15, 0, 1, 0, 3, 0, 5, 0, 7, 0, 9, 0, 11, 0, 13, 0, 15, 0, 1, 0, 3, 0, 5, 0, 7, 0, 9, 0, 11, 0, 13, 0, 15, 0, 1, 0, 3, 0, 5, 0, 7, 0]

sage: [power_mod(n,5,17)for n in xrange(0, 87)] #A070601    n^5 mod 17.

[0, 1, 15, 5, 4, 14, 7, 11, 9, 8, 6, 10, 3, 13, 12, 2, 16, 0, 1, 15, 5, 4, 14, 7, 11, 9, 8, 6, 10, 3, 13, 12, 2, 16, 0, 1, 15, 5, 4, 14, 7, 11, 9, 8, 6, 10, 3, 13, 12, 2, 16, 0, 1, 15, 5, 4, 14, 7, 11, 9, 8, 6, 10, 3, 13, 12, 2, 16, 0, 1, 15, 5, 4, 14, 7, 11, 9, 8, 6, 10, 3, 13, 12, 2, 16, 0, 1]

sage: [power_mod(n,5,18)for n in xrange(0, 87)] # ok A070602    n^5 mod 18.

[0, 1, 14, 9, 16, 11, 0, 13, 8, 9, 10, 5, 0, 7, 2, 9, 4, 17, 0, 1, 14, 9, 16, 11, 0, 13, 8, 9, 10, 5, 0, 7, 2, 9, 4, 17, 0, 1, 14, 9, 16, 11, 0, 13, 8, 9, 10, 5, 0, 7, 2, 9, 4, 17, 0, 1, 14, 9, 16, 11, 0, 13, 8, 9, 10, 5, 0, 7, 2, 9, 4, 17, 0, 1, 14, 9, 16, 11, 0, 13, 8, 9, 10, 5, 0, 7, 2]

sage: [power_mod(n,5,19)for n in xrange(0, 84)] #ok A070603   n^5 mod 19.

[0, 1, 13, 15, 17, 9, 5, 11, 12, 16, 3, 7, 8, 14, 10, 2, 4, 6, 18, 0, 1, 13, 15, 17, 9, 5, 11, 12, 16, 3, 7, 8, 14, 10, 2, 4, 6, 18, 0, 1, 13, 15, 17, 9, 5, 11, 12, 16, 3, 7, 8, 14, 10, 2, 4, 6, 18, 0, 1, 13, 15, 17, 9, 5, 11, 12, 16, 3, 7, 8, 14, 10, 2, 4, 6, 18, 0, 1, 13, 15, 17, 9, 5, 11]

sage: [power_mod(n,5,20)for n in xrange(0, 86)] #ok A070604    n^5 mod 20.

[0, 1, 12, 3, 4, 5, 16, 7, 8, 9, 0, 11, 12, 13, 4, 15, 16, 17, 8, 19, 0, 1, 12, 3, 4, 5, 16, 7, 8, 9, 0, 11, 12, 13, 4, 15, 16, 17, 8, 19, 0, 1, 12, 3, 4, 5, 16, 7, 8, 9, 0, 11, 12, 13, 4, 15, 16, 17, 8, 19, 0, 1, 12, 3, 4, 5, 16, 7, 8, 9, 0, 11, 12, 13, 4, 15, 16, 17, 8, 19, 0, 1, 12, 3, 4, 5]

sage: [power_mod(n,5,21)for n in xrange(0, 82)] # ok A070605    n^5 mod 21.

[0, 1, 11, 12, 16, 17, 6, 7, 8, 18, 19, 2, 3, 13, 14, 15, 4, 5, 9, 10, 20, 0, 1, 11, 12, 16, 17, 6, 7, 8, 18, 19, 2, 3, 13, 14, 15, 4, 5, 9, 10, 20, 0, 1, 11, 12, 16, 17, 6, 7, 8, 18, 19, 2, 3, 13, 14, 15, 4, 5, 9, 10, 20, 0, 1, 11, 12, 16, 17, 6, 7, 8, 18, 19, 2, 3, 13, 14, 15, 4, 5, 9]

sage: [power_mod(n,5,22)for n in xrange(0, 76)] #ok A070606    n^5 mod 22.

[0, 1, 10, 1, 12, 1, 10, 21, 10, 1, 10, 11, 12, 21, 12, 1, 12, 21, 10, 21, 12, 21, 0, 1, 10, 1, 12, 1, 10, 21, 10, 1, 10, 11, 12, 21, 12, 1, 12, 21, 10, 21, 12, 21, 0, 1, 10, 1, 12, 1, 10, 21, 10, 1, 10, 11, 12, 21, 12, 1, 12, 21, 10, 21, 12, 21, 0, 1, 10, 1, 12, 1, 10, 21, 10, 1]

sage: [power_mod(n,5,23)for n in xrange(0, 81)] #ok A070607    n^5 mod 23.

[0, 1, 9, 13, 12, 20, 2, 17, 16, 8, 19, 5, 18, 4, 15, 7, 6, 21, 3, 11, 10, 14, 22, 0, 1, 9, 13, 12, 20, 2, 17, 16, 8, 19, 5, 18, 4, 15, 7, 6, 21, 3, 11, 10, 14, 22, 0, 1, 9, 13, 12, 20, 2, 17, 16, 8, 19, 5, 18, 4, 15, 7, 6, 21, 3, 11, 10, 14, 22, 0, 1, 9, 13, 12, 20, 2, 17, 16, 8, 19, 5]

sage: [power_mod(n,5,24)for n in xrange(0, 84)] #ok A070486    a(n) = n^3 mod 24 (or equivalently, n^5 mod 24).

[0, 1, 8, 3, 16, 5, 0, 7, 8, 9, 16, 11, 0, 13, 8, 15, 16, 17, 0, 19, 8, 21, 16, 23, 0, 1, 8, 3, 16, 5, 0, 7, 8, 9, 16, 11, 0, 13, 8, 15, 16, 17, 0, 19, 8, 21, 16, 23, 0, 1, 8, 3, 16, 5, 0, 7, 8, 9, 16, 11, 0, 13, 8, 15, 16, 17, 0, 19, 8, 21, 16, 23, 0, 1, 8, 3, 16, 5, 0, 7, 8, 9, 16, 11]

sage: [power_mod(n,5,25)for n in xrange(0, 87)] # ok A070609   n^5 mod 25.

[0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1, 7, 18, 24, 0, 1]

sage: [power_mod(n,5,26)for n in xrange(0, 87)] #nnnnnnnnnnnnnn

[0, 1, 6, 9, 10, 5, 2, 11, 8, 3, 4, 7, 12, 13, 14, 19, 22, 23, 18, 15, 24, 21, 16, 17, 20, 25, 0, 1, 6, 9, 10, 5, 2, 11, 8, 3, 4, 7, 12, 13, 14, 19, 22, 23, 18, 15, 24, 21, 16, 17, 20, 25, 0, 1, 6, 9, 10, 5, 2, 11, 8, 3, 4, 7, 12, 13, 14, 19, 22, 23, 18, 15, 24, 21, 16, 17, 20, 25, 0, 1, 6, 9, 10, 5, 2, 11, 8]

sage: [power_mod(n,5,27)for n in xrange(0, 86)] #ok A070611   n^5 mod 27.

[0, 1, 5, 0, 25, 20, 0, 13, 17, 0, 19, 23, 0, 16, 11, 0, 4, 8, 0, 10, 14, 0, 7, 2, 0, 22, 26, 0, 1, 5, 0, 25, 20, 0, 13, 17, 0, 19, 23, 0, 16, 11, 0, 4, 8, 0, 10, 14, 0, 7, 2, 0, 22, 26, 0, 1, 5, 0, 25, 20, 0, 13, 17, 0, 19, 23, 0, 16, 11, 0, 4, 8, 0, 10, 14, 0, 7, 2, 0, 22, 26, 0, 1, 5, 0, 25]

sage: [power_mod(n,5,28)for n in xrange(0, 80)] #ok A070612    n^5 mod 28.

[0, 1, 4, 19, 16, 17, 20, 7, 8, 25, 12, 23, 24, 13, 0, 15, 4, 5, 16, 3, 20, 21, 8, 11, 12, 9, 24, 27, 0, 1, 4, 19, 16, 17, 20, 7, 8, 25, 12, 23, 24, 13, 0, 15, 4, 5, 16, 3, 20, 21, 8, 11, 12, 9, 24, 27, 0, 1, 4, 19, 16, 17, 20, 7, 8, 25, 12, 23, 24, 13, 0, 15, 4, 5, 16, 3, 20, 21, 8, 11]

sage: [power_mod(n,5,29)for n in xrange(0, 78)] #A070613    	 n^5 mod 29.

[0, 1, 3, 11, 9, 22, 4, 16, 27, 5, 8, 14, 12, 6, 19, 10, 23, 17, 15, 21, 24, 2, 13, 25, 7, 20, 18, 26, 28, 0, 1, 3, 11, 9, 22, 4, 16, 27, 5, 8, 14, 12, 6, 19, 10, 23, 17, 15, 21, 24, 2, 13, 25, 7, 20, 18, 26, 28, 0, 1, 3, 11, 9, 22, 4, 16, 27, 5, 8, 14, 12, 6, 19, 10, 23, 17, 15, 21]

sage: [power_mod(n,5,30)for n in xrange(0, 87)] #nem kell A001477    The nonnegative integers.

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26]

sage: [power_mod(n,5,31)for n in xrange(0, 84)] #ok A070614    n^5 mod 31.

[0, 1, 1, 26, 1, 25, 26, 5, 1, 25, 25, 6, 26, 6, 5, 30, 1, 26, 25, 5, 25, 6, 6, 30, 26, 5, 6, 30, 5, 30, 30, 0, 1, 1, 26, 1, 25, 26, 5, 1, 25, 25, 6, 26, 6, 5, 30, 1, 26, 25, 5, 25, 6, 6, 30, 26, 5, 6, 30, 5, 30, 30, 0, 1, 1, 26, 1, 25, 26, 5, 1, 25, 25, 6, 26, 6, 5, 30, 1, 26, 25, 5, 25, 6]

sage: [power_mod(n,5,32)for n in xrange(0, 84)] #nnnnnnnnn

[0, 1, 0, 19, 0, 21, 0, 7, 0, 9, 0, 27, 0, 29, 0, 15, 0, 17, 0, 3, 0, 5, 0, 23, 0, 25, 0, 11, 0, 13, 0, 31, 0, 1, 0, 19, 0, 21, 0, 7, 0, 9, 0, 27, 0, 29, 0, 15, 0, 17, 0, 3, 0, 5, 0, 23, 0, 25, 0, 11, 0, 13, 0, 31, 0, 1, 0, 19, 0, 21, 0, 7, 0, 9, 0, 27, 0, 29, 0, 15, 0, 17, 0, 3]

sage: [power_mod(n,5,34)for n in xrange(0, 77)] #ok A070617    n^5 mod 34.

[0, 1, 32, 5, 4, 31, 24, 11, 26, 25, 6, 27, 20, 13, 12, 19, 16, 17, 18, 15, 22, 21, 14, 7, 28, 9, 8, 23, 10, 3, 30, 29, 2, 33, 0, 1, 32, 5, 4, 31, 24, 11, 26, 25, 6, 27, 20, 13, 12, 19, 16, 17, 18, 15, 22, 21, 14, 7, 28, 9, 8, 23, 10, 3, 30, 29, 2, 33, 0, 1, 32, 5, 4, 31, 24, 11, 26]

sage: [power_mod(n,5,33)for n in xrange(0, 74)] #ok A070616    n^5 mod 33.

[0, 1, 32, 12, 1, 23, 21, 10, 32, 12, 10, 11, 12, 10, 23, 12, 1, 32, 21, 10, 23, 21, 22, 23, 21, 1, 23, 12, 10, 32, 21, 1, 32, 0, 1, 32, 12, 1, 23, 21, 10, 32, 12, 10, 11, 12, 10, 23, 12, 1, 32, 21, 10, 23, 21, 22, 23, 21, 1, 23, 12, 10, 32, 21, 1, 32, 0, 1, 32, 12, 1, 23, 21, 10]

sage: [power_mod(n,5,35)for n in xrange(0, 77)] # ok A070618  n^5 mod 35.

[0, 1, 32, 33, 9, 10, 6, 7, 8, 4, 5, 16, 17, 13, 14, 15, 11, 12, 23, 24, 20, 21, 22, 18, 19, 30, 31, 27, 28, 29, 25, 26, 2, 3, 34, 0, 1, 32, 33, 9, 10, 6, 7, 8, 4, 5, 16, 17, 13, 14, 15, 11, 12, 23, 24, 20, 21, 22, 18, 19, 30, 31, 27, 28, 29, 25, 26, 2, 3, 34, 0, 1, 32, 33, 9, 10, 6]

sage: [power_mod(n,5,36)for n in xrange(0, 82)] # A070619  n^5 mod 36.

[0, 1, 32, 27, 16, 29, 0, 31, 8, 9, 28, 23, 0, 25, 20, 27, 4, 17, 0, 19, 32, 9, 16, 11, 0, 13, 8, 27, 28, 5, 0, 7, 20, 9, 4, 35, 0, 1, 32, 27, 16, 29, 0, 31, 8, 9, 28, 23, 0, 25, 20, 27, 4, 17, 0, 19, 32, 9, 16, 11, 0, 13, 8, 27, 28, 5, 0, 7, 20, 9, 4, 35, 0, 1, 32, 27, 16, 29, 0, 31, 8, 9]

sage: [power_mod(n,5,37)for n in xrange(0, 76)] #ok A070620   n^5 mod 37.

[0, 1, 32, 21, 25, 17, 6, 9, 23, 34, 26, 27, 7, 35, 29, 24, 33, 19, 15, 22, 18, 4, 13, 8, 2, 30, 10, 11, 3, 14, 28, 31, 20, 12, 16, 5, 36, 0, 1, 32, 21, 25, 17, 6, 9, 23, 34, 26, 27, 7, 35, 29, 24, 33, 19, 15, 22, 18, 4, 13, 8, 2, 30, 10, 11, 3, 14, 28, 31, 20, 12, 16, 5, 36, 0, 1]

sage: [power_mod(n,5,39)for n in xrange(0, 76)] #ok A070622    n^5 mod 39.

[0, 1, 32, 9, 10, 5, 15, 37, 8, 3, 4, 20, 12, 13, 14, 6, 22, 23, 18, 28, 11, 21, 16, 17, 33, 25, 26, 27, 19, 35, 36, 31, 2, 24, 34, 29, 30, 7, 38, 0, 1, 32, 9, 10, 5, 15, 37, 8, 3, 4, 20, 12, 13, 14, 6, 22, 23, 18, 28, 11, 21, 16, 17, 33, 25, 26, 27, 19, 35, 36, 31, 2, 24, 34, 29, 30]

sage: [power_mod(n,5,38)for n in xrange(0, 76)] #ok A070621   n^5 mod 38.

[0, 1, 32, 15, 36, 9, 24, 11, 12, 35, 22, 7, 8, 33, 10, 21, 4, 25, 18, 19, 20, 13, 34, 17, 28, 5, 30, 31, 16, 3, 26, 27, 14, 29, 2, 23, 6, 37, 0, 1, 32, 15, 36, 9, 24, 11, 12, 35, 22, 7, 8, 33, 10, 21, 4, 25, 18, 19, 20, 13, 34, 17, 28, 5, 30, 31, 16, 3, 26, 27, 14, 29, 2, 23, 6, 37]

sage: [power_mod(n,5,40)for n in xrange(0, 77)] #A070623    n^5 mod 40.

[0, 1, 32, 3, 24, 5, 16, 7, 8, 9, 0, 11, 32, 13, 24, 15, 16, 17, 8, 19, 0, 21, 32, 23, 24, 25, 16, 27, 8, 29, 0, 31, 32, 33, 24, 35, 16, 37, 8, 39, 0, 1, 32, 3, 24, 5, 16, 7, 8, 9, 0, 11, 32, 13, 24, 15, 16, 17, 8, 19, 0, 21, 32, 23, 24, 25, 16, 27, 8, 29, 0, 31, 32, 33, 24, 35, 16]

sage: [power_mod(n,5,41)for n in xrange(0, 79)] #ok A070624  n^5 mod 41.

[0, 1, 32, 38, 40, 9, 27, 38, 9, 9, 1, 3, 3, 38, 27, 14, 1, 27, 1, 27, 32, 9, 14, 40, 14, 40, 27, 14, 3, 38, 38, 40, 32, 32, 3, 14, 32, 1, 3, 9, 40, 0, 1, 32, 38, 40, 9, 27, 38, 9, 9, 1, 3, 3, 38, 27, 14, 1, 27, 1, 27, 32, 9, 14, 40, 14, 40, 27, 14, 3, 38, 38, 40, 32, 32, 3, 14, 32, 1]

sage: [power_mod(n,5,43)for n in xrange(0, 75)] #ok A070626   n^5 mod 43.

[0, 1, 32, 28, 35, 29, 36, 37, 2, 10, 25, 16, 34, 31, 23, 38, 21, 40, 19, 30, 26, 4, 39, 17, 13, 24, 3, 22, 5, 20, 12, 9, 27, 18, 33, 41, 6, 7, 14, 8, 15, 11, 42, 0, 1, 32, 28, 35, 29, 36, 37, 2, 10, 25, 16, 34, 31, 23, 38, 21, 40, 19, 30, 26, 4, 39, 17, 13, 24, 3, 22, 5, 20, 12, 9]

sage: [power_mod(n,5,42)for n in xrange(0, 75)] #

[0, 1, 32, 33, 16, 17, 6, 7, 8, 39, 40, 23, 24, 13, 14, 15, 4, 5, 30, 31, 20, 21, 22, 11, 12, 37, 38, 27, 28, 29, 18, 19, 2, 3, 34, 35, 36, 25, 26, 9, 10, 41, 0, 1, 32, 33, 16, 17, 6, 7, 8, 39, 40, 23, 24, 13, 14, 15, 4, 5, 30, 31, 20, 21, 22, 11, 12, 37, 38, 27, 28, 29, 18, 19, 2]

sage: [power_mod(n,5,44)for n in xrange(0, 74)] #ok A070627   n^5 mod 44.

[0, 1, 32, 23, 12, 1, 32, 43, 32, 1, 32, 11, 12, 21, 12, 23, 12, 21, 32, 43, 12, 21, 0, 23, 32, 1, 12, 23, 32, 21, 32, 23, 32, 33, 12, 43, 12, 1, 12, 43, 32, 21, 12, 43, 0, 1, 32, 23, 12, 1, 32, 43, 32, 1, 32, 11, 12, 21, 12, 23, 12, 21, 32, 43, 12, 21, 0, 23, 32, 1, 12, 23, 32, 21]

sage: [power_mod(n,5,45)for n in xrange(0, 76)] #ok A070628    n^5 mod 45.

[0, 1, 32, 18, 34, 20, 36, 22, 8, 9, 10, 41, 27, 43, 29, 0, 31, 17, 18, 19, 5, 36, 7, 38, 9, 40, 26, 27, 28, 14, 0, 16, 2, 18, 4, 35, 36, 37, 23, 9, 25, 11, 27, 13, 44, 0, 1, 32, 18, 34, 20, 36, 22, 8, 9, 10, 41, 27, 43, 29, 0, 31, 17, 18, 19, 5, 36, 7, 38, 9, 40, 26, 27, 28, 14, 0]

sage: [power_mod(n,5,46)for n in xrange(0, 75)] #ok A070629    n^5 mod 46.

[0, 1, 32, 13, 12, 43, 2, 17, 16, 31, 42, 5, 18, 27, 38, 7, 6, 21, 26, 11, 10, 37, 22, 23, 24, 9, 36, 35, 20, 25, 40, 39, 8, 19, 28, 41, 4, 15, 30, 29, 44, 3, 34, 33, 14, 45, 0, 1, 32, 13, 12, 43, 2, 17, 16, 31, 42, 5, 18, 27, 38, 7, 6, 21, 26, 11, 10, 37, 22, 23, 24, 9, 36, 35, 20]

sage: [power_mod(n,5,47)for n in xrange(0, 75)] #ok A070630    n^5 mod 47.

[0, 1, 32, 8, 37, 23, 21, 28, 9, 17, 31, 29, 14, 40, 3, 43, 6, 34, 27, 45, 5, 36, 35, 22, 25, 12, 11, 42, 2, 20, 13, 41, 4, 44, 7, 33, 18, 16, 30, 38, 19, 26, 24, 10, 39, 15, 46, 0, 1, 32, 8, 37, 23, 21, 28, 9, 17, 31, 29, 14, 40, 3, 43, 6, 34, 27, 45, 5, 36, 35, 22, 25, 12, 11, 42]

sage: [power_mod(n,5,48)for n in xrange(0, 77)] #ok A070631    n^5 mod 48.

[0, 1, 32, 3, 16, 5, 0, 7, 32, 9, 16, 11, 0, 13, 32, 15, 16, 17, 0, 19, 32, 21, 16, 23, 0, 25, 32, 27, 16, 29, 0, 31, 32, 33, 16, 35, 0, 37, 32, 39, 16, 41, 0, 43, 32, 45, 16, 47, 0, 1, 32, 3, 16, 5, 0, 7, 32, 9, 16, 11, 0, 13, 32, 15, 16, 17, 0, 19, 32, 21, 16, 23, 0, 25, 32, 27, 16]

sage: [power_mod(n,5,49)for n in xrange(0, 76)] #ok új n^5 mod 49. A167527 n^5 mod 49.

[0, 1, 32, 47, 44, 38, 34, 0, 36, 4, 40, 37, 10, 20, 0, 22, 25, 33, 30, 31, 6, 0, 8, 46, 26, 23, 3, 41, 0, 43, 18, 19, 16, 24, 27, 0, 29, 39, 12, 9, 45, 13, 0, 15, 11, 5, 2, 17, 48, 0, 1, 32, 47, 44, 38, 34, 0, 36, 4, 40, 37, 10, 20, 0, 22, 25, 33, 30, 31, 6, 0, 8, 46, 26, 23, 3]

sage: [power_mod(n,5,50)for n in xrange(0, 80)] #ok új n^5 mod 50.A167528 n^5 mod 50.

[0, 1, 32, 43, 24, 25, 26, 7, 18, 49, 0, 1, 32, 43, 24, 25, 26, 7, 18, 49, 0, 1, 32, 43, 24, 25, 26, 7, 18, 49, 0, 1, 32, 43, 24, 25, 26, 7, 18, 49, 0, 1, 32, 43, 24, 25, 26, 7, 18, 49, 0, 1, 32, 43, 24, 25, 26, 7, 18, 49, 0, 1, 32, 43, 24, 25, 26, 7, 18, 49, 0, 1, 32, 43, 24, 25, 26, 7, 18, 49]

sage: [power_mod(2,-n,7)for n in xrange(0, 105)] #ok A153727  	 	 Trajectory of 3x+1 sequence starting at 1.

[1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2]

sage: [power_mod(2,n,7)for n in xrange(0, 105)] #ok A069705  	 	 2^n mod 7.

[1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4, 1, 2, 4]

sage: [power_mod(2,-n,5)for n in xrange(0, 101)] #ok A070352  3^n mod 5.

[1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1]

sage: [power_mod(2,n,5)for n in xrange(0, 105)] #ok A070402   2^n mod 5.

[1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1, 2, 4, 3, 1]

sage: [power_mod(2,n,6)for n in xrange(0, 105)] #nnnnn

[1, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4]

sage: [power_mod(2,-n,6)for n in xrange(0, 105)] #n

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_8.py", line 5, in <module> exec compile(ur'[power_mod(_sage_const_2 ,-n,_sage_const_6 )for n in xrange(_sage_const_0 , _sage_const_105 )] #n' + '\n', '', 'single') File "", line 1, in <module> File "/sage/sage/local/lib/python2.6/site-packages/sage/rings/arith.py", line 1614, in power_mod ainv = inverse_mod(a,m) File "/sage/sage/local/lib/python2.6/site-packages/sage/rings/arith.py", line 1523, in inverse_mod return a.inverse_mod(m) File "integer.pyx", line 4803, in sage.rings.integer.Integer.inverse_mod (sage/rings/integer.c:27366) ZeroDivisionError: Inverse does not exist.

sage: [power_mod(2,n,8)for n in xrange(0, 105)] #ok A069705  	 	 2^n mod 7.

[1, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

sage: [power_mod(3,n,5)for n in xrange(0, 105)] #okA070352  3^n mod 5.

[1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1, 3, 4, 2, 1]

[0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1, 5, 0, 7, 2, 0, 4, 8, 0, 1]

sage: [power_mod(n,5,11)for n in xrange(0, 85)] #ok A070596  n^5 mod 11.

[0, 1, 10, 1, 1, 1, 10, 10, 10, 1, 10, 0, 1, 10, 1, 1, 1, 10, 10, 10, 1, 10, 0, 1, 10, 1, 1, 1, 10, 10, 10, 1, 10, 0, 1, 10, 1, 1, 1, 10, 10, 10, 1, 10, 0, 1, 10, 1, 1, 1, 10, 10, 10, 1, 10, 0, 1, 10, 1, 1, 1, 10, 10, 10, 1, 10, 0, 1, 10, 1, 1, 1, 10, 10, 10, 1, 10, 0, 1, 10, 1, 1, 1, 10, 10]

sage: [power_mod(2*n,5+n,11)for n in xrange(0, 85)] #nnnnnnnnnnnnnn

[0, 9, 5, 4, 7, 1, 1, 9, 4, 3, 1, 0, 7, 9, 2, 1, 10, 1, 5, 9, 10, 9, 0, 3, 3, 1, 8, 1, 1, 4, 1, 4, 4, 0, 6, 1, 6, 9, 10, 1, 1, 5, 6, 3, 0, 1, 4, 3, 6, 1, 1, 3, 3, 9, 5, 0, 2, 5, 7, 4, 10, 1, 9, 4, 8, 1, 0, 4, 9, 9, 10, 1, 1, 5, 9, 1, 9, 0, 8, 3, 10, 3, 10, 1, 4]

sage: [power_mod(n,6,n+1)for n in xrange(0, 10)] #

[0, 1, 1, 1, 1, 1, 1, 1, 1, 1]

sage: [power_mod(n,6,1)for n in xrange(0, 101)] #

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

sage: [power_mod(n,6,2)for n in xrange(0, 101)] #

[0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]

sage: [power_mod(n,6,3)for n in xrange(0, 101)] #ok A011655    Periodic sequence 0,1,1,..n^6 mod 3.

[0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1]

sage: [power_mod(n,6,4)for n in xrange(0, 101)] #nem kell

[0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]

sage: [power_mod(n,2,5)for n in xrange(0, 101)] #ok A070430    n^2 mod 5.        + + Equivalently n^6 mod 5.

[0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0]

sage: [power_mod(n,6,5)for n in xrange(0, 101)] #ok A070430    n^2 mod 5.        + + Equivalently n^6 mod 5.

[0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0, 1, 4, 4, 1, 0]

sage: [power_mod(n,6,6)for n in xrange(0, 101)] #okA070431   n^2 mod 6. A070511   n^4 mod 6. >>Equivalently n^6 mod 6.

[0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4]

sage: [power_mod(n,6,7)for n in xrange(0, 105)] #okA109720  	 	 Periodic sequence {0,1,1,1,1,1,1} or n^6 mod 7.

[0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1]

sage: [power_mod(n,6,8)for n in xrange(0, 105)] #nem kelll

[0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]

sage: [power_mod(n,6,9)for n in xrange(0, 105)] #ok A011655 Periodic sequence 0,1,1,...    (n^6 mod 3.volt)

[0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1]

sage: [power_mod(n,6,10)for n in xrange(0, 81)] #ok A008959   Final digits of squares. n^6 mod 10.

[0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0]

sage: [power_mod(n,6,11)for n in xrange(0, 101)] #ok A070634   n^6 mod 11.

[0, 1, 9, 3, 4, 5, 5, 4, 3, 9, 1, 0, 1, 9, 3, 4, 5, 5, 4, 3, 9, 1, 0, 1, 9, 3, 4, 5, 5, 4, 3, 9, 1, 0, 1, 9, 3, 4, 5, 5, 4, 3, 9, 1, 0, 1, 9, 3, 4, 5, 5, 4, 3, 9, 1, 0, 1, 9, 3, 4, 5, 5, 4, 3, 9, 1, 0, 1, 9, 3, 4, 5, 5, 4, 3, 9, 1, 0, 1, 9, 3, 4, 5, 5, 4, 3, 9, 1, 0, 1, 9, 3, 4, 5, 5, 4, 3, 9, 1, 0, 1]

sage: [power_mod(n,6,12)for n in xrange(0, 101)] #ok A070435   n^2 mod 12.

[0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4]

sage: [power_mod(n,180,12)for n in xrange(0, 101)] # A070435 n^z mod 12, if z even number. Example:n^180 mod 12. etc...

[0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4]

sage: [power_mod(n,6,13)for n in xrange(0, 84)] #ok A070636    n^6 mod 13.

[0, 1, 12, 1, 1, 12, 12, 12, 12, 1, 1, 12, 1, 0, 1, 12, 1, 1, 12, 12, 12, 12, 1, 1, 12, 1, 0, 1, 12, 1, 1, 12, 12, 12, 12, 1, 1, 12, 1, 0, 1, 12, 1, 1, 12, 12, 12, 12, 1, 1, 12, 1, 0, 1, 12, 1, 1, 12, 12, 12, 12, 1, 1, 12, 1, 0, 1, 12, 1, 1, 12, 12, 12, 12, 1, 1, 12, 1, 0, 1, 12, 1, 1, 12]

sage: [power_mod(n,6,14)for n in xrange(0, 101)] #ok A070637  	   n^6 mod 14.

[0, 1, 8, 1, 8, 1, 8, 7, 8, 1, 8, 1, 8, 1, 0, 1, 8, 1, 8, 1, 8, 7, 8, 1, 8, 1, 8, 1, 0, 1, 8, 1, 8, 1, 8, 7, 8, 1, 8, 1, 8, 1, 0, 1, 8, 1, 8, 1, 8, 7, 8, 1, 8, 1, 8, 1, 0, 1, 8, 1, 8, 1, 8, 7, 8, 1, 8, 1, 8, 1, 0, 1, 8, 1, 8, 1, 8, 7, 8, 1, 8, 1, 8, 1, 0, 1, 8, 1, 8, 1, 8, 7, 8, 1, 8, 1, 8, 1, 0, 1, 8]

sage: [power_mod(n,6,15)for n in xrange(0, 197)] #ok A070638    n^6 mod 15. A070438    n^2 mod 15.

[0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1]

sage: [power_mod(n,6,16)for n in xrange(0, 105)] #ok új n^6 mod 16.

[0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0]

sage: [power_mod(n,6,17)for n in xrange(0, 88)] #ok A070640  	 	 n^6 mod 17.

[0, 1, 13, 15, 16, 2, 8, 9, 4, 4, 9, 8, 2, 16, 15, 13, 1, 0, 1, 13, 15, 16, 2, 8, 9, 4, 4, 9, 8, 2, 16, 15, 13, 1, 0, 1, 13, 15, 16, 2, 8, 9, 4, 4, 9, 8, 2, 16, 15, 13, 1, 0, 1, 13, 15, 16, 2, 8, 9, 4, 4, 9, 8, 2, 16, 15, 13, 1, 0, 1, 13, 15, 16, 2, 8, 9, 4, 4, 9, 8, 2, 16, 15, 13, 1, 0, 1, 13]

sage: [power_mod(n,6,18)for n in xrange(0, 90)] #ok A070641    n^6 mod 18.

[0, 1, 10, 9, 10, 1, 0, 1, 10, 9, 10, 1, 0, 1, 10, 9, 10, 1, 0, 1, 10, 9, 10, 1, 0, 1, 10, 9, 10, 1, 0, 1, 10, 9, 10, 1, 0, 1, 10, 9, 10, 1, 0, 1, 10, 9, 10, 1, 0, 1, 10, 9, 10, 1, 0, 1, 10, 9, 10, 1, 0, 1, 10, 9, 10, 1, 0, 1, 10, 9, 10, 1, 0, 1, 10, 9, 10, 1, 0, 1, 10, 9, 10, 1, 0, 1, 10, 9, 10, 1]

sage: [power_mod(n,6,19)for n in xrange(0, 90)] #ok A070642    n^6 mod 19.

[0, 1, 7, 7, 11, 7, 11, 1, 1, 11, 11, 1, 1, 11, 7, 11, 7, 7, 1, 0, 1, 7, 7, 11, 7, 11, 1, 1, 11, 11, 1, 1, 11, 7, 11, 7, 7, 1, 0, 1, 7, 7, 11, 7, 11, 1, 1, 11, 11, 1, 1, 11, 7, 11, 7, 7, 1, 0, 1, 7, 7, 11, 7, 11, 1, 1, 11, 11, 1, 1, 11, 7, 11, 7, 7, 1, 0, 1, 7, 7, 11, 7, 11, 1, 1, 11, 11, 1, 1, 11]

sage: [power_mod(n,6,20)for n in xrange(0, 95)] #okA070442 n^2 mod 20. Also, n^6 mod 20.

[0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16]

sage: [power_mod(n,6,21)for n in xrange(0, 90)] #ok A070644  n^6 mod 21.

[0, 1, 1, 15, 1, 1, 15, 7, 1, 15, 1, 1, 15, 1, 7, 15, 1, 1, 15, 1, 1, 0, 1, 1, 15, 1, 1, 15, 7, 1, 15, 1, 1, 15, 1, 7, 15, 1, 1, 15, 1, 1, 0, 1, 1, 15, 1, 1, 15, 7, 1, 15, 1, 1, 15, 1, 7, 15, 1, 1, 15, 1, 1, 0, 1, 1, 15, 1, 1, 15, 7, 1, 15, 1, 1, 15, 1, 7, 15, 1, 1, 15, 1, 1, 0, 1, 1, 15, 1, 1]

sage: [power_mod(n,6,22)for n in xrange(0, 82)] #ok A070645    n^6 mod 22.

[0, 1, 20, 3, 4, 5, 16, 15, 14, 9, 12, 11, 12, 9, 14, 15, 16, 5, 4, 3, 20, 1, 0, 1, 20, 3, 4, 5, 16, 15, 14, 9, 12, 11, 12, 9, 14, 15, 16, 5, 4, 3, 20, 1, 0, 1, 20, 3, 4, 5, 16, 15, 14, 9, 12, 11, 12, 9, 14, 15, 16, 5, 4, 3, 20, 1, 0, 1, 20, 3, 4, 5, 16, 15, 14, 9, 12, 11, 12, 9, 14, 15]

sage: [power_mod(n,6,23)for n in xrange(0, 89)] #ok A070646    n^6 mod 23.

[0, 1, 18, 16, 2, 8, 12, 4, 13, 3, 6, 9, 9, 6, 3, 13, 4, 12, 8, 2, 16, 18, 1, 0, 1, 18, 16, 2, 8, 12, 4, 13, 3, 6, 9, 9, 6, 3, 13, 4, 12, 8, 2, 16, 18, 1, 0, 1, 18, 16, 2, 8, 12, 4, 13, 3, 6, 9, 9, 6, 3, 13, 4, 12, 8, 2, 16, 18, 1, 0, 1, 18, 16, 2, 8, 12, 4, 13, 3, 6, 9, 9, 6, 3, 13, 4, 12, 8, 2]

sage: [power_mod(n,6,24)for n in xrange(0, 90)] #ok A070567   n^4 mod 24. A070567 Equivalently n^6 mod 24.

[0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1]

sage: [power_mod(n,6,25)for n in xrange(0, 84)] #ok A070648    n^6 mod 25.

[0, 1, 14, 4, 21, 0, 6, 24, 19, 16, 0, 11, 9, 9, 11, 0, 16, 19, 24, 6, 0, 21, 4, 14, 1, 0, 1, 14, 4, 21, 0, 6, 24, 19, 16, 0, 11, 9, 9, 11, 0, 16, 19, 24, 6, 0, 21, 4, 14, 1, 0, 1, 14, 4, 21, 0, 6, 24, 19, 16, 0, 11, 9, 9, 11, 0, 16, 19, 24, 6, 0, 21, 4, 14, 1, 0, 1, 14, 4, 21, 0, 6, 24, 19]

sage: [power_mod(n,6,26)for n in xrange(0, 75)] #okA070649 	 n^6 mod 26.

[0, 1, 12, 1, 14, 25, 12, 25, 12, 1, 14, 25, 14, 13, 14, 25, 14, 1, 12, 25, 12, 25, 14, 1, 12, 1, 0, 1, 12, 1, 14, 25, 12, 25, 12, 1, 14, 25, 14, 13, 14, 25, 14, 1, 12, 25, 12, 25, 14, 1, 12, 1, 0, 1, 12, 1, 14, 25, 12, 25, 12, 1, 14, 25, 14, 13, 14, 25, 14, 1, 12, 25, 12, 25, 14]

sage: [power_mod(n,6,27)for n in xrange(0, 85)] #ok A070650   n^6 mod 27.

[0, 1, 10, 0, 19, 19, 0, 10, 1, 0, 1, 10, 0, 19, 19, 0, 10, 1, 0, 1, 10, 0, 19, 19, 0, 10, 1, 0, 1, 10, 0, 19, 19, 0, 10, 1, 0, 1, 10, 0, 19, 19, 0, 10, 1, 0, 1, 10, 0, 19, 19, 0, 10, 1, 0, 1, 10, 0, 19, 19, 0, 10, 1, 0, 1, 10, 0, 19, 19, 0, 10, 1, 0, 1, 10, 0, 19, 19, 0, 10, 1, 0, 1, 10, 0]

sage: [power_mod(n,6,28)for n in xrange(0, 101)] #ok A070651   n^6 mod 28.

[0, 1, 8, 1, 8, 1, 8, 21, 8, 1, 8, 1, 8, 1, 0, 1, 8, 1, 8, 1, 8, 21, 8, 1, 8, 1, 8, 1, 0, 1, 8, 1, 8, 1, 8, 21, 8, 1, 8, 1, 8, 1, 0, 1, 8, 1, 8, 1, 8, 21, 8, 1, 8, 1, 8, 1, 0, 1, 8, 1, 8, 1, 8, 21, 8, 1, 8, 1, 8, 1, 0, 1, 8, 1, 8, 1, 8, 21, 8, 1, 8, 1, 8, 1, 0, 1, 8, 1, 8, 1, 8, 21, 8, 1, 8, 1, 8, 1, 0, 1, 8]

sage: [power_mod(n,6,29)for n in xrange(0, 81)] #ok A070652    n^6 mod 29.

[0, 1, 6, 4, 7, 23, 24, 25, 13, 16, 22, 9, 28, 20, 5, 5, 20, 28, 9, 22, 16, 13, 25, 24, 23, 7, 4, 6, 1, 0, 1, 6, 4, 7, 23, 24, 25, 13, 16, 22, 9, 28, 20, 5, 5, 20, 28, 9, 22, 16, 13, 25, 24, 23, 7, 4, 6, 1, 0, 1, 6, 4, 7, 23, 24, 25, 13, 16, 22, 9, 28, 20, 5, 5, 20, 28, 9, 22, 16, 13, 25]

sage: [power_mod(n,6,30)for n in xrange(0, 80)] #okA070452 n^2 mod 30.A070653n^6 mod 30. nov.3

[0, 1, 4, 9, 16, 25, 6, 19, 4, 21, 10, 1, 24, 19, 16, 15, 16, 19, 24, 1, 10, 21, 4, 19, 6, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 6, 19, 4, 21, 10, 1, 24, 19, 16, 15, 16, 19, 24, 1, 10, 21, 4, 19, 6, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 6, 19, 4, 21, 10, 1, 24, 19, 16, 15, 16, 19, 24, 1]

sage: [power_mod(n,6,31)for n in xrange(0, 96)] #ok A070654  n^6 mod 31.

[0, 1, 2, 16, 4, 1, 1, 4, 8, 8, 2, 4, 2, 16, 8, 16, 16, 8, 16, 2, 4, 2, 8, 8, 4, 1, 1, 4, 16, 2, 1, 0, 1, 2, 16, 4, 1, 1, 4, 8, 8, 2, 4, 2, 16, 8, 16, 16, 8, 16, 2, 4, 2, 8, 8, 4, 1, 1, 4, 16, 2, 1, 0, 1, 2, 16, 4, 1, 1, 4, 8, 8, 2, 4, 2, 16, 8, 16, 16, 8, 16, 2, 4, 2, 8, 8, 4, 1, 1, 4, 16, 2, 1, 0, 1, 2]

sage: [power_mod(n,6,32)for n in xrange(0, 100)] #új n^6 mod 32. A167624 n^6 mod 32.

[0, 1, 0, 25, 0, 9, 0, 17, 0, 17, 0, 9, 0, 25, 0, 1, 0, 1, 0, 25, 0, 9, 0, 17, 0, 17, 0, 9, 0, 25, 0, 1, 0, 1, 0, 25, 0, 9, 0, 17, 0, 17, 0, 9, 0, 25, 0, 1, 0, 1, 0, 25, 0, 9, 0, 17, 0, 17, 0, 9, 0, 25, 0, 1, 0, 1, 0, 25, 0, 9, 0, 17, 0, 17, 0, 9, 0, 25, 0, 1, 0, 1, 0, 25, 0, 9, 0, 17, 0, 17, 0, 9, 0, 25, 0, 1, 0, 1, 0, 25]

sage: [power_mod(n,6,33)for n in xrange(0, 80)] #ok A070656    n^6 mod 33.

[0, 1, 31, 3, 4, 16, 27, 4, 25, 9, 1, 22, 12, 31, 25, 15, 16, 16, 15, 25, 31, 12, 22, 1, 9, 25, 4, 27, 16, 4, 3, 31, 1, 0, 1, 31, 3, 4, 16, 27, 4, 25, 9, 1, 22, 12, 31, 25, 15, 16, 16, 15, 25, 31, 12, 22, 1, 9, 25, 4, 27, 16, 4, 3, 31, 1, 0, 1, 31, 3, 4, 16, 27, 4, 25, 9, 1, 22, 12, 31]

sage: [power_mod(n,6,34)for n in xrange(0, 77)] #ok A070657    n^6 mod 34.

[0, 1, 30, 15, 16, 19, 8, 9, 4, 21, 26, 25, 2, 33, 32, 13, 18, 17, 18, 13, 32, 33, 2, 25, 26, 21, 4, 9, 8, 19, 16, 15, 30, 1, 0, 1, 30, 15, 16, 19, 8, 9, 4, 21, 26, 25, 2, 33, 32, 13, 18, 17, 18, 13, 32, 33, 2, 25, 26, 21, 4, 9, 8, 19, 16, 15, 30, 1, 0, 1, 30, 15, 16, 19, 8, 9, 4]

sage: [power_mod(n,6,35)for n in xrange(0, 80)] #ok A070658    n^6 mod 35.

[0, 1, 29, 29, 1, 15, 1, 14, 29, 1, 15, 1, 29, 29, 21, 15, 1, 29, 29, 1, 15, 21, 29, 29, 1, 15, 1, 29, 14, 1, 15, 1, 29, 29, 1, 0, 1, 29, 29, 1, 15, 1, 14, 29, 1, 15, 1, 29, 29, 21, 15, 1, 29, 29, 1, 15, 21, 29, 29, 1, 15, 1, 29, 14, 1, 15, 1, 29, 29, 1, 0, 1, 29, 29, 1, 15, 1, 14, 29, 1]

sage: [power_mod(n,6,36)for n in xrange(0, 90)] #ok A070659  	  n^6 mod 36.

[0, 1, 28, 9, 28, 1, 0, 1, 28, 9, 28, 1, 0, 1, 28, 9, 28, 1, 0, 1, 28, 9, 28, 1, 0, 1, 28, 9, 28, 1, 0, 1, 28, 9, 28, 1, 0, 1, 28, 9, 28, 1, 0, 1, 28, 9, 28, 1, 0, 1, 28, 9, 28, 1, 0, 1, 28, 9, 28, 1, 0, 1, 28, 9, 28, 1, 0, 1, 28, 9, 28, 1, 0, 1, 28, 9, 28, 1, 0, 1, 28, 9, 28, 1, 0, 1, 28, 9, 28, 1]

sage: [power_mod(n,6,37)for n in xrange(0, 73)] #ok A070660    n^6 mod 37.

[0, 1, 27, 26, 26, 11, 36, 26, 36, 10, 1, 1, 10, 11, 36, 27, 10, 27, 11, 11, 27, 10, 27, 36, 11, 10, 1, 1, 10, 36, 26, 36, 11, 26, 26, 27, 1, 0, 1, 27, 26, 26, 11, 36, 26, 36, 10, 1, 1, 10, 11, 36, 27, 10, 27, 11, 11, 27, 10, 27, 36, 11, 10, 1, 1, 10, 36, 26, 36, 11, 26, 26, 27]

sage: [power_mod(n,6,38)for n in xrange(0, 79)] #ok A070661    n^6 mod 38.

[0, 1, 26, 7, 30, 7, 30, 1, 20, 11, 30, 1, 20, 11, 26, 11, 26, 7, 20, 19, 20, 7, 26, 11, 26, 11, 20, 1, 30, 11, 20, 1, 30, 7, 30, 7, 26, 1, 0, 1, 26, 7, 30, 7, 30, 1, 20, 11, 30, 1, 20, 11, 26, 11, 26, 7, 20, 19, 20, 7, 26, 11, 26, 11, 20, 1, 30, 11, 20, 1, 30, 7, 30, 7, 26, 1, 0, 1, 26]

sage: [power_mod(n,6,39)for n in xrange(0, 77)] #okA070662 n^6 mod 39.

[0, 1, 25, 27, 1, 25, 12, 25, 25, 27, 1, 25, 27, 13, 1, 12, 1, 1, 12, 25, 25, 12, 1, 1, 12, 1, 13, 27, 25, 1, 27, 25, 25, 12, 25, 1, 27, 25, 1, 0, 1, 25, 27, 1, 25, 12, 25, 25, 27, 1, 25, 27, 13, 1, 12, 1, 1, 12, 25, 25, 12, 1, 1, 12, 1, 13, 27, 25, 1, 27, 25, 25, 12, 25, 1, 27, 25]

sage: [power_mod(n,6,40)for n in xrange(0, 84)] #okA070663    n^6 mod 40.

[0, 1, 24, 9, 16, 25, 16, 9, 24, 1, 0, 1, 24, 9, 16, 25, 16, 9, 24, 1, 0, 1, 24, 9, 16, 25, 16, 9, 24, 1, 0, 1, 24, 9, 16, 25, 16, 9, 24, 1, 0, 1, 24, 9, 16, 25, 16, 9, 24, 1, 0, 1, 24, 9, 16, 25, 16, 9, 24, 1, 0, 1, 24, 9, 16, 25, 16, 9, 24, 1, 0, 1, 24, 9, 16, 25, 16, 9, 24, 1, 0, 1, 24, 9]

sage: [power_mod(n,6,41)for n in xrange(0, 78)] #ok A070664    n^6 mod 41.

[0, 1, 23, 32, 37, 4, 39, 20, 31, 40, 10, 33, 36, 2, 9, 5, 16, 8, 18, 21, 25, 25, 21, 18, 8, 16, 5, 9, 2, 36, 33, 10, 40, 31, 20, 39, 4, 37, 32, 23, 1, 0, 1, 23, 32, 37, 4, 39, 20, 31, 40, 10, 33, 36, 2, 9, 5, 16, 8, 18, 21, 25, 25, 21, 18, 8, 16, 5, 9, 2, 36, 33, 10, 40, 31, 20, 39, 4]

sage: [power_mod(n,6,42)for n in xrange(0, 78)] #ok A070665    n^6 mod 42.

[0, 1, 22, 15, 22, 1, 36, 7, 22, 15, 22, 1, 36, 1, 28, 15, 22, 1, 36, 1, 22, 21, 22, 1, 36, 1, 22, 15, 28, 1, 36, 1, 22, 15, 22, 7, 36, 1, 22, 15, 22, 1, 0, 1, 22, 15, 22, 1, 36, 7, 22, 15, 22, 1, 36, 1, 28, 15, 22, 1, 36, 1, 22, 21, 22, 1, 36, 1, 22, 15, 28, 1, 36, 1, 22, 15, 22, 7]

sage: [power_mod(n,6,43)for n in xrange(0, 77)] #ok A070666    n^6 mod 43.

[0, 1, 21, 41, 11, 16, 1, 1, 16, 4, 35, 4, 21, 16, 21, 11, 35, 35, 41, 11, 4, 41, 41, 4, 11, 41, 35, 35, 11, 21, 16, 21, 4, 35, 4, 16, 1, 1, 16, 11, 41, 21, 1, 0, 1, 21, 41, 11, 16, 1, 1, 16, 4, 35, 4, 21, 16, 21, 11, 35, 35, 41, 11, 4, 41, 41, 4, 11, 41, 35, 35, 11, 21, 16, 21, 4, 35]

sage: [power_mod(n,100,10)for n in xrange(0, 81)] #okA070514    n^4 mod 10.

[0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0]

sage: [power_mod(n,10,10)for n in xrange(0, 81)] #ok A008959   Final digits of squares.

[0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, 6, 9, 4, 1, 0]

sage: [power_mod(n,7,5)for n in xrange(0, 101)] #ok

sage: [power_mod(n,7,6)for n in xrange(0, 101)] #ok A010875    Simple periodic sequence.

[0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4]

sage: [power_mod(n,7,7)for n in xrange(0, 81)] #ok A010876    Simple periodic sequence.

[0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3]

sage: [power_mod(n,7,8)for n in xrange(0, 101)] #okA109753    n^3 mod 8; the periodic sequence {0,1,0,3,0,5,0,7}.

[0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0]

sage: [power_mod(n,7,9)for n in xrange(0, 101)] #A070692    n^7 mod 9.

[0, 1, 2, 0, 4, 5, 0, 7, 8, 0, 1, 2, 0, 4, 5, 0, 7, 8, 0, 1, 2, 0, 4, 5, 0, 7, 8, 0, 1, 2, 0, 4, 5, 0, 7, 8, 0, 1, 2, 0, 4, 5, 0, 7, 8, 0, 1, 2, 0, 4, 5, 0, 7, 8, 0, 1, 2, 0, 4, 5, 0, 7, 8, 0, 1, 2, 0, 4, 5, 0, 7, 8, 0, 1, 2, 0, 4, 5, 0, 7, 8, 0, 1, 2, 0, 4, 5, 0, 7, 8, 0, 1, 2, 0, 4, 5, 0, 7, 8, 0, 1]

sage: [power_mod(n,7,10)for n in xrange(0, 90)] #ok A008960 Final digits of cubes.

[0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9]

sage: [power_mod(n,7,11)for n in xrange(0, 99)] #ok A070693  	 n^7 mod 11.

[0, 1, 7, 9, 5, 3, 8, 6, 2, 4, 10, 0, 1, 7, 9, 5, 3, 8, 6, 2, 4, 10, 0, 1, 7, 9, 5, 3, 8, 6, 2, 4, 10, 0, 1, 7, 9, 5, 3, 8, 6, 2, 4, 10, 0, 1, 7, 9, 5, 3, 8, 6, 2, 4, 10, 0, 1, 7, 9, 5, 3, 8, 6, 2, 4, 10, 0, 1, 7, 9, 5, 3, 8, 6, 2, 4, 10, 0, 1, 7, 9, 5, 3, 8, 6, 2, 4, 10, 0, 1, 7, 9, 5, 3, 8, 6, 2, 4, 10]

sage: [power_mod(n,7,12)for n in xrange(0, 100)] #ok. A070474   n^3 mod 12.  ok. A070597   n^5 mod 12.

[0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3]

sage: [power_mod(n,7,13)for n in xrange(0, 93)] # okA070695  n^7 mod 13. ok

[0, 1, 11, 3, 4, 8, 7, 6, 5, 9, 10, 2, 12, 0, 1, 11, 3, 4, 8, 7, 6, 5, 9, 10, 2, 12, 0, 1, 11, 3, 4, 8, 7, 6, 5, 9, 10, 2, 12, 0, 1, 11, 3, 4, 8, 7, 6, 5, 9, 10, 2, 12, 0, 1, 11, 3, 4, 8, 7, 6, 5, 9, 10, 2, 12, 0, 1, 11, 3, 4, 8, 7, 6, 5, 9, 10, 2, 12, 0, 1, 11, 3, 4, 8, 7, 6, 5, 9, 10, 2, 12, 0, 1]

sage: [power_mod(n,7,14)for n in xrange(0, 93)] #ok A070696  	 n^7 mod 14.

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8]

sage: [power_mod(n,7,15)for n in xrange(0, 90)] #ok A070477  	   n^3 mod 15.

[0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14]

sage: [power_mod(n,7,16)for n in xrange(0, 90)] #ok A167166    n^7 mod 16.  	

Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 29 2009

[0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9]

sage: [power_mod(n,7,17)for n in xrange(0, 90)] #ok A070699   	 n^7 mod 17.

[0, 1, 9, 11, 13, 10, 14, 12, 15, 2, 5, 3, 7, 4, 6, 8, 16, 0, 1, 9, 11, 13, 10, 14, 12, 15, 2, 5, 3, 7, 4, 6, 8, 16, 0, 1, 9, 11, 13, 10, 14, 12, 15, 2, 5, 3, 7, 4, 6, 8, 16, 0, 1, 9, 11, 13, 10, 14, 12, 15, 2, 5, 3, 7, 4, 6, 8, 16, 0, 1, 9, 11, 13, 10, 14, 12, 15, 2, 5, 3, 7, 4, 6, 8, 16, 0, 1, 9, 11, 13]

sage: [power_mod(n,3,15)for n in xrange(0, 90)] #ok A070477  	  n^3 mod 15.

[0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14]

sage: [power_mod(n,3,16)for n in xrange(0, 96)] #okA070478  	  n^3 mod 16.

[0, 1, 8, 11, 0, 13, 8, 7, 0, 9, 8, 3, 0, 5, 8, 15, 0, 1, 8, 11, 0, 13, 8, 7, 0, 9, 8, 3, 0, 5, 8, 15, 0, 1, 8, 11, 0, 13, 8, 7, 0, 9, 8, 3, 0, 5, 8, 15, 0, 1, 8, 11, 0, 13, 8, 7, 0, 9, 8, 3, 0, 5, 8, 15, 0, 1, 8, 11, 0, 13, 8, 7, 0, 9, 8, 3, 0, 5, 8, 15, 0, 1, 8, 11, 0, 13, 8, 7, 0, 9, 8, 3, 0, 5, 8, 15]

sage: [power_mod(n,7,16)for n in xrange(0, 93)] #ok új  A167166 Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 29 2009

[0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0]

sage: [power_mod(n,7,17)for n in xrange(0, 86)] #okA070699  	 	 n^7 mod 17.

[0, 1, 9, 11, 13, 10, 14, 12, 15, 2, 5, 3, 7, 4, 6, 8, 16, 0, 1, 9, 11, 13, 10, 14, 12, 15, 2, 5, 3, 7, 4, 6, 8, 16, 0, 1, 9, 11, 13, 10, 14, 12, 15, 2, 5, 3, 7, 4, 6, 8, 16, 0, 1, 9, 11, 13, 10, 14, 12, 15, 2, 5, 3, 7, 4, 6, 8, 16, 0, 1, 9, 11, 13, 10, 14, 12, 15, 2, 5, 3, 7, 4, 6, 8, 16, 0]

sage: [power_mod(n,7,18)for n in xrange(0, 90)] #ok A070700  	 	 n^7 mod 18.

[0, 1, 2, 9, 4, 5, 0, 7, 8, 9, 10, 11, 0, 13, 14, 9, 16, 17, 0, 1, 2, 9, 4, 5, 0, 7, 8, 9, 10, 11, 0, 13, 14, 9, 16, 17, 0, 1, 2, 9, 4, 5, 0, 7, 8, 9, 10, 11, 0, 13, 14, 9, 16, 17, 0, 1, 2, 9, 4, 5, 0, 7, 8, 9, 10, 11, 0, 13, 14, 9, 16, 17, 0, 1, 2, 9, 4, 5, 0, 7, 8, 9, 10, 11, 0, 13, 14, 9, 16, 17]

sage: [power_mod(n,7,19)for n in xrange(0, 85)] #ok A070701  	  n^7 mod 19.

[0, 1, 14, 2, 6, 16, 9, 7, 8, 4, 15, 11, 12, 10, 3, 13, 17, 5, 18, 0, 1, 14, 2, 6, 16, 9, 7, 8, 4, 15, 11, 12, 10, 3, 13, 17, 5, 18, 0, 1, 14, 2, 6, 16, 9, 7, 8, 4, 15, 11, 12, 10, 3, 13, 17, 5, 18, 0, 1, 14, 2, 6, 16, 9, 7, 8, 4, 15, 11, 12, 10, 3, 13, 17, 5, 18, 0, 1, 14, 2, 6, 16, 9, 7, 8]

sage: [power_mod(n,3,20)for n in xrange(0, 85)] #ok A070482   	 n^3 mod 20. A070702    n^7 mod 20.

[0, 1, 8, 7, 4, 5, 16, 3, 12, 9, 0, 11, 8, 17, 4, 15, 16, 13, 12, 19, 0, 1, 8, 7, 4, 5, 16, 3, 12, 9, 0, 11, 8, 17, 4, 15, 16, 13, 12, 19, 0, 1, 8, 7, 4, 5, 16, 3, 12, 9, 0, 11, 8, 17, 4, 15, 16, 13, 12, 19, 0, 1, 8, 7, 4, 5, 16, 3, 12, 9, 0, 11, 8, 17, 4, 15, 16, 13, 12, 19, 0, 1, 8, 7, 4]

sage: [power_mod(n,7,20)for n in xrange(0, 85)] #ok A070482     n^3 mod 20.  A070702    n^7 mod 20.  1. sage: [power_mod(n,3,20)for n in xrange(0, 85)] #
2. sage: [power_mod(n,7,20)for n in xrange(0, 85)] #

[0, 1, 8, 7, 4, 5, 16, 3, 12, 9, 0, 11, 8, 17, 4, 15, 16, 13, 12, 19, 0, 1, 8, 7, 4, 5, 16, 3, 12, 9, 0, 11, 8, 17, 4, 15, 16, 13, 12, 19, 0, 1, 8, 7, 4, 5, 16, 3, 12, 9, 0, 11, 8, 17, 4, 15, 16, 13, 12, 19, 0, 1, 8, 7, 4, 5, 16, 3, 12, 9, 0, 11, 8, 17, 4, 15, 16, 13, 12, 19, 0, 1, 8, 7, 4]

sage: [power_mod(n,7,21)for n in xrange(0, 85)] #nnnnnnn n^7 mod 21.

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0]

sage: [power_mod(n,7,22)for n in xrange(0, 82)] #ok A070703     n^7 mod 22.

[0, 1, 18, 9, 16, 3, 8, 17, 2, 15, 10, 11, 12, 7, 20, 5, 14, 19, 6, 13, 4, 21, 0, 1, 18, 9, 16, 3, 8, 17, 2, 15, 10, 11, 12, 7, 20, 5, 14, 19, 6, 13, 4, 21, 0, 1, 18, 9, 16, 3, 8, 17, 2, 15, 10, 11, 12, 7, 20, 5, 14, 19, 6, 13, 4, 21, 0, 1, 18, 9, 16, 3, 8, 17, 2, 15, 10, 11, 12, 7, 20, 5]

sage: [power_mod(n,7,23)for n in xrange(0, 82)] #ok A070704    n^7 mod 23.

[0, 1, 13, 2, 8, 17, 3, 5, 12, 4, 14, 7, 16, 9, 19, 11, 18, 20, 6, 15, 21, 10, 22, 0, 1, 13, 2, 8, 17, 3, 5, 12, 4, 14, 7, 16, 9, 19, 11, 18, 20, 6, 15, 21, 10, 22, 0, 1, 13, 2, 8, 17, 3, 5, 12, 4, 14, 7, 16, 9, 19, 11, 18, 20, 6, 15, 21, 10, 22, 0, 1, 13, 2, 8, 17, 3, 5, 12, 4, 14, 7, 16]

sage: [power_mod(n,3,24)for n in xrange(0, 86)] #okA070486    a(n) = n^3 mod 24 (or equivalently, n^5 mod 24).

[0, 1, 8, 3, 16, 5, 0, 7, 8, 9, 16, 11, 0, 13, 8, 15, 16, 17, 0, 19, 8, 21, 16, 23, 0, 1, 8, 3, 16, 5, 0, 7, 8, 9, 16, 11, 0, 13, 8, 15, 16, 17, 0, 19, 8, 21, 16, 23, 0, 1, 8, 3, 16, 5, 0, 7, 8, 9, 16, 11, 0, 13, 8, 15, 16, 17, 0, 19, 8, 21, 16, 23, 0, 1, 8, 3, 16, 5, 0, 7, 8, 9, 16, 11, 0, 13]

sage: [power_mod(n,5,24)for n in xrange(0, 86)] #okA070486    a(n) = n^3 mod 24 (or equivalently, n^5 mod 24).

[0, 1, 8, 3, 16, 5, 0, 7, 8, 9, 16, 11, 0, 13, 8, 15, 16, 17, 0, 19, 8, 21, 16, 23, 0, 1, 8, 3, 16, 5, 0, 7, 8, 9, 16, 11, 0, 13, 8, 15, 16, 17, 0, 19, 8, 21, 16, 23, 0, 1, 8, 3, 16, 5, 0, 7, 8, 9, 16, 11, 0, 13, 8, 15, 16, 17, 0, 19, 8, 21, 16, 23, 0, 1, 8, 3, 16, 5, 0, 7, 8, 9, 16, 11, 0, 13]

sage: [power_mod(n,7,24)for n in xrange(0, 86)] #okA070486    a(n) = n^3 mod 24 (or equivalently, n^5 mod 24).

[0, 1, 8, 3, 16, 5, 0, 7, 8, 9, 16, 11, 0, 13, 8, 15, 16, 17, 0, 19, 8, 21, 16, 23, 0, 1, 8, 3, 16, 5, 0, 7, 8, 9, 16, 11, 0, 13, 8, 15, 16, 17, 0, 19, 8, 21, 16, 23, 0, 1, 8, 3, 16, 5, 0, 7, 8, 9, 16, 11, 0, 13, 8, 15, 16, 17, 0, 19, 8, 21, 16, 23, 0, 1, 8, 3, 16, 5, 0, 7, 8, 9, 16, 11, 0, 13]

sage: [power_mod(n,7,25)for n in xrange(0, 84)] # ok A070706  	   n^7 mod 25.

[0, 1, 3, 12, 9, 0, 11, 18, 2, 19, 0, 21, 8, 17, 4, 0, 6, 23, 7, 14, 0, 16, 13, 22, 24, 0, 1, 3, 12, 9, 0, 11, 18, 2, 19, 0, 21, 8, 17, 4, 0, 6, 23, 7, 14, 0, 16, 13, 22, 24, 0, 1, 3, 12, 9, 0, 11, 18, 2, 19, 0, 21, 8, 17, 4, 0, 6, 23, 7, 14, 0, 16, 13, 22, 24, 0, 1, 3, 12, 9, 0, 11, 18, 2]

sage: [power_mod(n,7,26)for n in xrange(0, 80)] #ok A070707  	   n^7 mod 26.

[0, 1, 24, 3, 4, 21, 20, 19, 18, 9, 10, 15, 12, 13, 14, 11, 16, 17, 8, 7, 6, 5, 22, 23, 2, 25, 0, 1, 24, 3, 4, 21, 20, 19, 18, 9, 10, 15, 12, 13, 14, 11, 16, 17, 8, 7, 6, 5, 22, 23, 2, 25, 0, 1, 24, 3, 4, 21, 20, 19, 18, 9, 10, 15, 12, 13, 14, 11, 16, 17, 8, 7, 6, 5, 22, 23, 2, 25, 0, 1]

sage: [power_mod(n,7,27)for n in xrange(0, 85)] # ok A070708  	  n^7 mod 27.

[0, 1, 20, 0, 22, 14, 0, 16, 8, 0, 10, 2, 0, 4, 23, 0, 25, 17, 0, 19, 11, 0, 13, 5, 0, 7, 26, 0, 1, 20, 0, 22, 14, 0, 16, 8, 0, 10, 2, 0, 4, 23, 0, 25, 17, 0, 19, 11, 0, 13, 5, 0, 7, 26, 0, 1, 20, 0, 22, 14, 0, 16, 8, 0, 10, 2, 0, 4, 23, 0, 25, 17, 0, 19, 11, 0, 13, 5, 0, 7, 26, 0, 1, 20, 0]

sage: [power_mod(n,7,28)for n in xrange(0, 81)] #ok A070709 	 n^7 mod 28.

[0, 1, 16, 3, 4, 5, 20, 7, 8, 9, 24, 11, 12, 13, 0, 15, 16, 17, 4, 19, 20, 21, 8, 23, 24, 25, 12, 27, 0, 1, 16, 3, 4, 5, 20, 7, 8, 9, 24, 11, 12, 13, 0, 15, 16, 17, 4, 19, 20, 21, 8, 23, 24, 25, 12, 27, 0, 1, 16, 3, 4, 5, 20, 7, 8, 9, 24, 11, 12, 13, 0, 15, 16, 17, 4, 19, 20, 21, 8, 23, 24]

sage: [power_mod(n,7,29)for n in xrange(0, 76)] #ok A070710  n^7 mod 29.

[0, 1, 12, 12, 28, 28, 28, 1, 17, 28, 17, 12, 17, 28, 12, 17, 1, 12, 17, 12, 1, 12, 28, 1, 1, 1, 17, 17, 28, 0, 1, 12, 12, 28, 28, 28, 1, 17, 28, 17, 12, 17, 28, 12, 17, 1, 12, 17, 12, 1, 12, 28, 1, 1, 1, 17, 17, 28, 0, 1, 12, 12, 28, 28, 28, 1, 17, 28, 17, 12, 17, 28, 12, 17, 1, 12]

sage: [power_mod(n,3,30)for n in xrange(0, 78)] #

[0, 1, 8, 27, 4, 5, 6, 13, 2, 9, 10, 11, 18, 7, 14, 15, 16, 23, 12, 19, 20, 21, 28, 17, 24, 25, 26, 3, 22, 29, 0, 1, 8, 27, 4, 5, 6, 13, 2, 9, 10, 11, 18, 7, 14, 15, 16, 23, 12, 19, 20, 21, 28, 17, 24, 25, 26, 3, 22, 29, 0, 1, 8, 27, 4, 5, 6, 13, 2, 9, 10, 11, 18, 7, 14, 15, 16, 23]

sage: [power_mod(n,7,30)for n in xrange(0, 78)] #ok A070492  	 	 n^3 mod 30.

[0, 1, 8, 27, 4, 5, 6, 13, 2, 9, 10, 11, 18, 7, 14, 15, 16, 23, 12, 19, 20, 21, 28, 17, 24, 25, 26, 3, 22, 29, 0, 1, 8, 27, 4, 5, 6, 13, 2, 9, 10, 11, 18, 7, 14, 15, 16, 23, 12, 19, 20, 21, 28, 17, 24, 25, 26, 3, 22, 29, 0, 1, 8, 27, 4, 5, 6, 13, 2, 9, 10, 11, 18, 7, 14, 15, 16, 23]

sage: [power_mod(n,7,31)for n in xrange(0, 77)] #ok A070712   	 n^7 mod 31.

[0, 1, 4, 17, 16, 5, 6, 28, 2, 10, 20, 13, 24, 22, 19, 23, 8, 12, 9, 7, 18, 11, 21, 29, 3, 25, 26, 15, 14, 27, 30, 0, 1, 4, 17, 16, 5, 6, 28, 2, 10, 20, 13, 24, 22, 19, 23, 8, 12, 9, 7, 18, 11, 21, 29, 3, 25, 26, 15, 14, 27, 30, 0, 1, 4, 17, 16, 5, 6, 28, 2, 10, 20, 13, 24, 22, 19]

sage: [power_mod(n,7,32)for n in xrange(0, 82)] #nnnnnnn új új új 	 	 n^7 mod 32.

[0, 1, 0, 11, 0, 13, 0, 23, 0, 25, 0, 3, 0, 5, 0, 15, 0, 17, 0, 27, 0, 29, 0, 7, 0, 9, 0, 19, 0, 21, 0, 31, 0, 1, 0, 11, 0, 13, 0, 23, 0, 25, 0, 3, 0, 5, 0, 15, 0, 17, 0, 27, 0, 29, 0, 7, 0, 9, 0, 19, 0, 21, 0, 31, 0, 1, 0, 11, 0, 13, 0, 23, 0, 25, 0, 3, 0, 5, 0, 15, 0, 17]

sage: [power_mod(n,7,33)for n in xrange(0, 77)] #ok  A070714    n^7 mod 33.

[0, 1, 29, 9, 16, 14, 30, 28, 2, 15, 10, 11, 12, 7, 20, 27, 25, 8, 6, 13, 26, 21, 22, 23, 18, 31, 5, 3, 19, 17, 24, 4, 32, 0, 1, 29, 9, 16, 14, 30, 28, 2, 15, 10, 11, 12, 7, 20, 27, 25, 8, 6, 13, 26, 21, 22, 23, 18, 31, 5, 3, 19, 17, 24, 4, 32, 0, 1, 29, 9, 16, 14, 30, 28, 2, 15, 10]

sage: [power_mod(n,7,34)for n in xrange(0, 77)] #ok A070715  	   n^7 mod 34.

[0, 1, 26, 11, 30, 27, 14, 29, 32, 19, 22, 3, 24, 21, 6, 25, 16, 17, 18, 9, 28, 13, 10, 31, 12, 15, 2, 5, 20, 7, 4, 23, 8, 33, 0, 1, 26, 11, 30, 27, 14, 29, 32, 19, 22, 3, 24, 21, 6, 25, 16, 17, 18, 9, 28, 13, 10, 31, 12, 15, 2, 5, 20, 7, 4, 23, 8, 33, 0, 1, 26, 11, 30, 27, 14, 29, 32]

sage: [power_mod(n,7,35)for n in xrange(0, 77)] #ok A070716   	 n^7 mod 35.

[0, 1, 23, 17, 4, 5, 6, 28, 22, 9, 10, 11, 33, 27, 14, 15, 16, 3, 32, 19, 20, 21, 8, 2, 24, 25, 26, 13, 7, 29, 30, 31, 18, 12, 34, 0, 1, 23, 17, 4, 5, 6, 28, 22, 9, 10, 11, 33, 27, 14, 15, 16, 3, 32, 19, 20, 21, 8, 2, 24, 25, 26, 13, 7, 29, 30, 31, 18, 12, 34, 0, 1, 23, 17, 4, 5, 6]

sage: [power_mod(n,7,36)for n in xrange(0, 84)] #ok A070717  	  n^7 mod 36.

[0, 1, 20, 27, 4, 5, 0, 7, 8, 9, 28, 11, 0, 13, 32, 27, 16, 17, 0, 19, 20, 9, 4, 23, 0, 25, 8, 27, 28, 29, 0, 31, 32, 9, 16, 35, 0, 1, 20, 27, 4, 5, 0, 7, 8, 9, 28, 11, 0, 13, 32, 27, 16, 17, 0, 19, 20, 9, 4, 23, 0, 25, 8, 27, 28, 29, 0, 31, 32, 9, 16, 35, 0, 1, 20, 27, 4, 5, 0, 7, 8, 9, 28, 11]

sage: [power_mod(n,7,37)for n in xrange(0, 77)] #ok A070718  	  n^7 mod 37.

[0, 1, 17, 4, 30, 18, 31, 34, 29, 16, 10, 11, 9, 32, 23, 35, 12, 15, 13, 24, 22, 25, 2, 14, 5, 28, 26, 27, 21, 8, 3, 6, 19, 7, 33, 20, 36, 0, 1, 17, 4, 30, 18, 31, 34, 29, 16, 10, 11, 9, 32, 23, 35, 12, 15, 13, 24, 22, 25, 2, 14, 5, 28, 26, 27, 21, 8, 3, 6, 19, 7, 33, 20, 36, 0, 1, 17]

sage: [power_mod(n,7,38)for n in xrange(0, 76)] #ok A070719    n^7 mod 38.

[0, 1, 14, 21, 6, 35, 28, 7, 8, 23, 34, 11, 12, 29, 22, 13, 36, 5, 18, 19, 20, 33, 2, 25, 16, 9, 26, 27, 4, 15, 30, 31, 10, 3, 32, 17, 24, 37, 0, 1, 14, 21, 6, 35, 28, 7, 8, 23, 34, 11, 12, 29, 22, 13, 36, 5, 18, 19, 20, 33, 2, 25, 16, 9, 26, 27, 4, 15, 30, 31, 10, 3, 32, 17, 24, 37]

sage: [power_mod(n,7,39)for n in xrange(0, 76)] #ok A070720  	  n^7 mod 39.

[0, 1, 11, 3, 4, 8, 33, 19, 5, 9, 10, 2, 12, 13, 14, 24, 16, 17, 21, 7, 32, 18, 22, 23, 15, 25, 26, 27, 37, 29, 30, 34, 20, 6, 31, 35, 36, 28, 38, 0, 1, 11, 3, 4, 8, 33, 19, 5, 9, 10, 2, 12, 13, 14, 24, 16, 17, 21, 7, 32, 18, 22, 23, 15, 25, 26, 27, 37, 29, 30, 34, 20, 6, 31, 35, 36]

sage: [power_mod(n,7,40)for n in xrange(0, 77)] # ok A070721  	  n^7 mod 40.

[0, 1, 8, 27, 24, 5, 16, 23, 32, 9, 0, 11, 8, 37, 24, 15, 16, 33, 32, 19, 0, 21, 8, 7, 24, 25, 16, 3, 32, 29, 0, 31, 8, 17, 24, 35, 16, 13, 32, 39, 0, 1, 8, 27, 24, 5, 16, 23, 32, 9, 0, 11, 8, 37, 24, 15, 16, 33, 32, 19, 0, 21, 8, 7, 24, 25, 16, 3, 32, 29, 0, 31, 8, 17, 24, 35, 16]

sage: [power_mod(n,7,41)for n in xrange(0, 75)] #ok A070722  	  n^7 mod 41.

[0, 1, 5, 14, 25, 20, 29, 17, 2, 32, 18, 35, 22, 26, 3, 34, 10, 13, 37, 30, 8, 33, 11, 4, 28, 31, 7, 38, 15, 19, 6, 23, 9, 39, 24, 12, 21, 16, 27, 36, 40, 0, 1, 5, 14, 25, 20, 29, 17, 2, 32, 18, 35, 22, 26, 3, 34, 10, 13, 37, 30, 8, 33, 11, 4, 28, 31, 7, 38, 15, 19, 6, 23, 9, 39]

sage: [power_mod(n,7,42)for n in xrange(  0, 76)] #új  n^7 mod 42.

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33]

sage: [power_mod(n,7,43)for n in xrange(0, 82)] # ok A070723  	  n^7 mod 43.

[0, 1, 42, 37, 1, 37, 6, 7, 42, 36, 6, 1, 37, 36, 36, 36, 1, 36, 7, 37, 37, 1, 42, 6, 6, 36, 7, 42, 7, 7, 7, 6, 42, 37, 7, 1, 36, 37, 6, 42, 6, 1, 42, 0, 1, 42, 37, 1, 37, 6, 7, 42, 36, 6, 1, 37, 36, 36, 36, 1, 36, 7, 37, 37, 1, 42, 6, 6, 36, 7, 42, 7, 7, 7, 6, 42, 37, 7, 1, 36, 37, 6]

sage: [power_mod(n,7,44)for n in xrange(0, 76)] # ok A070724  	   n^7 mod 44.

[0, 1, 40, 31, 16, 25, 8, 39, 24, 37, 32, 11, 12, 29, 20, 27, 36, 41, 28, 35, 4, 21, 0, 23, 40, 9, 16, 3, 8, 17, 24, 15, 32, 33, 12, 7, 20, 5, 36, 19, 28, 13, 4, 43, 0, 1, 40, 31, 16, 25, 8, 39, 24, 37, 32, 11, 12, 29, 20, 27, 36, 41, 28, 35, 4, 21, 0, 23, 40, 9, 16, 3, 8, 17, 24, 15]

sage: [power_mod(n,7,45)for n in xrange(0, 77)] # ok A070725    n^7 mod 45.

[0, 1, 38, 27, 4, 5, 36, 43, 17, 9, 10, 11, 18, 22, 14, 0, 16, 8, 27, 19, 20, 36, 13, 32, 9, 25, 26, 18, 37, 29, 0, 31, 23, 27, 34, 35, 36, 28, 2, 9, 40, 41, 18, 7, 44, 0, 1, 38, 27, 4, 5, 36, 43, 17, 9, 10, 11, 18, 22, 14, 0, 16, 8, 27, 19, 20, 36, 13, 32, 9, 25, 26, 18, 37, 29, 0, 31]

sage: [power_mod(n,7,46)for n in xrange(0, 75)] #ok A070726  	  n^7 mod 46.

[0, 1, 36, 25, 8, 17, 26, 5, 12, 27, 14, 7, 16, 9, 42, 11, 18, 43, 6, 15, 44, 33, 22, 23, 24, 13, 2, 31, 40, 3, 28, 35, 4, 37, 30, 39, 32, 19, 34, 41, 20, 29, 38, 21, 10, 45, 0, 1, 36, 25, 8, 17, 26, 5, 12, 27, 14, 7, 16, 9, 42, 11, 18, 43, 6, 15, 44, 33, 22, 23, 24, 13, 2, 31, 40]

sage: [power_mod(n,7,47)for n in xrange(0, 74)] # ok A070727   	 n^7 mod 47.

[0, 1, 34, 25, 28, 11, 4, 9, 12, 14, 45, 31, 42, 39, 24, 40, 32, 3, 6, 30, 26, 37, 20, 29, 18, 27, 10, 21, 17, 41, 44, 15, 7, 23, 8, 5, 16, 2, 33, 35, 38, 43, 36, 19, 22, 13, 46, 0, 1, 34, 25, 28, 11, 4, 9, 12, 14, 45, 31, 42, 39, 24, 40, 32, 3, 6, 30, 26, 37, 20, 29, 18, 27, 10]

sage: [power_mod(n,7,48)for n in xrange(0, 76)] #ok  A070728  n^7 mod 48.

[0, 1, 32, 27, 16, 29, 0, 7, 32, 9, 16, 35, 0, 37, 32, 15, 16, 17, 0, 43, 32, 45, 16, 23, 0, 25, 32, 3, 16, 5, 0, 31, 32, 33, 16, 11, 0, 13, 32, 39, 16, 41, 0, 19, 32, 21, 16, 47, 0, 1, 32, 27, 16, 29, 0, 7, 32, 9, 16, 35, 0, 37, 32, 15, 16, 17, 0, 43, 32, 45, 16, 23, 0, 25, 32, 3]

sage: [power_mod(n,7,49)for n in xrange(0, 76)] #nnnnnnnnnnnnnnn

[0, 1, 30, 31, 18, 19, 48, 0, 1, 30, 31, 18, 19, 48, 0, 1, 30, 31, 18, 19, 48, 0, 1, 30, 31, 18, 19, 48, 0, 1, 30, 31, 18, 19, 48, 0, 1, 30, 31, 18, 19, 48, 0, 1, 30, 31, 18, 19, 48, 0, 1, 30, 31, 18, 19, 48, 0, 1, 30, 31, 18, 19, 48, 0, 1, 30, 31, 18, 19, 48, 0, 1, 30, 31, 18, 19]

sage: [power_mod(n,3,3 )for n in xrange(0, 105)] # ok A010872  	   n mod 3.

[0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2]

sage: [power_mod(n,7,5 )for n in xrange(0, 1222)] #

[0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1]

sage: [power_mod(n,3,5 )for n in xrange(0, 1222)] #

[0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1]

sage: [power_mod(n,3,5 )for n in xrange(0, 101)] #A070471   n^3 mod 5. A070690    n^7 mod 5.

[0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0, 1, 3, 2, 4, 0]

sage: [power_mod(n,3,4 )for n in xrange(0, 105)]#ok A109718 Periodic sequence with period {0,1,0,3}, or n^3 mod 4.

[0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0]

sage: [power_mod(n,3,6 )for n in xrange(0, 81)] #ok A010875     Simple periodic sequence.

[0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2]

sage: [power_mod(n,3,7 )for n in xrange(0, 101)] # ok A070472    n^3 mod 7.

[0, 1, 1, 6, 1, 6, 6, 0, 1, 1, 6, 1, 6, 6, 0, 1, 1, 6, 1, 6, 6, 0, 1, 1, 6, 1, 6, 6, 0, 1, 1, 6, 1, 6, 6, 0, 1, 1, 6, 1, 6, 6, 0, 1, 1, 6, 1, 6, 6, 0, 1, 1, 6, 1, 6, 6, 0, 1, 1, 6, 1, 6, 6, 0, 1, 1, 6, 1, 6, 6, 0, 1, 1, 6, 1, 6, 6, 0, 1, 1, 6, 1, 6, 6, 0, 1, 1, 6, 1, 6, 6, 0, 1, 1, 6, 1, 6, 6, 0, 1, 1]

sage: [power_mod(n,3,19 )for n in xrange(0, 85)] #ok ? A070481  	  n^3 mod 19.

[0, 1, 8, 8, 7, 11, 7, 1, 18, 7, 12, 1, 18, 12, 8, 12, 11, 11, 18, 0, 1, 8, 8, 7, 11, 7, 1, 18, 7, 12, 1, 18, 12, 8, 12, 11, 11, 18, 0, 1, 8, 8, 7, 11, 7, 1, 18, 7, 12, 1, 18, 12, 8, 12, 11, 11, 18, 0, 1, 8, 8, 7, 11, 7, 1, 18, 7, 12, 1, 18, 12, 8, 12, 11, 11, 18, 0, 1, 8, 8, 7, 11, 7, 1, 18]

sage: [power_mod(n,3,8 )for n in xrange(0, 105)] #

[0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 0, 3, 0, 5, 0, 7, 0]

sage: [power_mod(n,3,9 )for n in xrange(0, 105)] # új n^3 mod 9

[0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8, 0, 1, 8]

sage: [power_mod(n,3,10 )for n in xrange(0, 81)] #ok A008960   Final digits of cubes.

[0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0, 1, 8, 7, 4, 5, 6, 3, 2, 9, 0]

sage: [power_mod(n,3,11 )for n in xrange(0, 99)] #ok A070473  	 	 n^3 mod 11.

[0, 1, 8, 5, 9, 4, 7, 2, 6, 3, 10, 0, 1, 8, 5, 9, 4, 7, 2, 6, 3, 10, 0, 1, 8, 5, 9, 4, 7, 2, 6, 3, 10, 0, 1, 8, 5, 9, 4, 7, 2, 6, 3, 10, 0, 1, 8, 5, 9, 4, 7, 2, 6, 3, 10, 0, 1, 8, 5, 9, 4, 7, 2, 6, 3, 10, 0, 1, 8, 5, 9, 4, 7, 2, 6, 3, 10, 0, 1, 8, 5, 9, 4, 7, 2, 6, 3, 10, 0, 1, 8, 5, 9, 4, 7, 2, 6, 3, 10]

sage: [power_mod(n,3,13 )for n in xrange(0, 93)] #ok A070475  	 	 n^3 mod 13.

[0, 1, 8, 1, 12, 8, 8, 5, 5, 1, 12, 5, 12, 0, 1, 8, 1, 12, 8, 8, 5, 5, 1, 12, 5, 12, 0, 1, 8, 1, 12, 8, 8, 5, 5, 1, 12, 5, 12, 0, 1, 8, 1, 12, 8, 8, 5, 5, 1, 12, 5, 12, 0, 1, 8, 1, 12, 8, 8, 5, 5, 1, 12, 5, 12, 0, 1, 8, 1, 12, 8, 8, 5, 5, 1, 12, 5, 12, 0, 1, 8, 1, 12, 8, 8, 5, 5, 1, 12, 5, 12, 0, 1]

sage: [power_mod(n,3,12 )for n in xrange(0, 100)] #ok előbb elment A070474  	 	 n^3 mod 12.

[0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3]

sage: [power_mod(n,3,14 )for n in xrange(0, 94)] # ok A070476  n^3 mod 14.

[0, 1, 8, 13, 8, 13, 6, 7, 8, 1, 6, 1, 6, 13, 0, 1, 8, 13, 8, 13, 6, 7, 8, 1, 6, 1, 6, 13, 0, 1, 8, 13, 8, 13, 6, 7, 8, 1, 6, 1, 6, 13, 0, 1, 8, 13, 8, 13, 6, 7, 8, 1, 6, 1, 6, 13, 0, 1, 8, 13, 8, 13, 6, 7, 8, 1, 6, 1, 6, 13, 0, 1, 8, 13, 8, 13, 6, 7, 8, 1, 6, 1, 6, 13, 0, 1, 8, 13, 8, 13, 6, 7, 8, 1]

sage: [power_mod(n,3,15 )for n in xrange(0, 90)] #ok A 070477    n^3 mod 15.

[0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14, 0, 1, 8, 12, 4, 5, 6, 13, 2, 9, 10, 11, 3, 7, 14]

sage: [power_mod(n,3,16 )for n in xrange(0, 96)] #ok korábban A070478  	  n^3 mod 16.

[0, 1, 8, 11, 0, 13, 8, 7, 0, 9, 8, 3, 0, 5, 8, 15, 0, 1, 8, 11, 0, 13, 8, 7, 0, 9, 8, 3, 0, 5, 8, 15, 0, 1, 8, 11, 0, 13, 8, 7, 0, 9, 8, 3, 0, 5, 8, 15, 0, 1, 8, 11, 0, 13, 8, 7, 0, 9, 8, 3, 0, 5, 8, 15, 0, 1, 8, 11, 0, 13, 8, 7, 0, 9, 8, 3, 0, 5, 8, 15, 0, 1, 8, 11, 0, 13, 8, 7, 0, 9, 8, 3, 0, 5, 8, 15]

sage: [power_mod(n,3,17 )for n in xrange(0, 87)] # ok A070479    n^3 mod 17.

[0, 1, 8, 10, 13, 6, 12, 3, 2, 15, 14, 5, 11, 4, 7, 9, 16, 0, 1, 8, 10, 13, 6, 12, 3, 2, 15, 14, 5, 11, 4, 7, 9, 16, 0, 1, 8, 10, 13, 6, 12, 3, 2, 15, 14, 5, 11, 4, 7, 9, 16, 0, 1, 8, 10, 13, 6, 12, 3, 2, 15, 14, 5, 11, 4, 7, 9, 16, 0, 1, 8, 10, 13, 6, 12, 3, 2, 15, 14, 5, 11, 4, 7, 9, 16, 0, 1]

sage: [power_mod(n,3,18 )for n in xrange(0, 90)] #ok A070480  	  n^3 mod 18.

[0, 1, 8, 9, 10, 17, 0, 1, 8, 9, 10, 17, 0, 1, 8, 9, 10, 17, 0, 1, 8, 9, 10, 17, 0, 1, 8, 9, 10, 17, 0, 1, 8, 9, 10, 17, 0, 1, 8, 9, 10, 17, 0, 1, 8, 9, 10, 17, 0, 1, 8, 9, 10, 17, 0, 1, 8, 9, 10, 17, 0, 1, 8, 9, 10, 17, 0, 1, 8, 9, 10, 17, 0, 1, 8, 9, 10, 17, 0, 1, 8, 9, 10, 17, 0, 1, 8, 9, 10, 17]

sage: [power_mod(n,3,20 )for n in xrange(0, 86)] #ok A070482    n^3 mod 20.

[0, 1, 8, 7, 4, 5, 16, 3, 12, 9, 0, 11, 8, 17, 4, 15, 16, 13, 12, 19, 0, 1, 8, 7, 4, 5, 16, 3, 12, 9, 0, 11, 8, 17, 4, 15, 16, 13, 12, 19, 0, 1, 8, 7, 4, 5, 16, 3, 12, 9, 0, 11, 8, 17, 4, 15, 16, 13, 12, 19, 0, 1, 8, 7, 4, 5, 16, 3, 12, 9, 0, 11, 8, 17, 4, 15, 16, 13, 12, 19, 0, 1, 8, 7, 4, 5]

sage: [power_mod(n,3,21 )for n in xrange(0, 84)] # ok A070483  	  n^3 mod 21.

[0, 1, 8, 6, 1, 20, 6, 7, 8, 15, 13, 8, 6, 13, 14, 15, 1, 20, 15, 13, 20, 0, 1, 8, 6, 1, 20, 6, 7, 8, 15, 13, 8, 6, 13, 14, 15, 1, 20, 15, 13, 20, 0, 1, 8, 6, 1, 20, 6, 7, 8, 15, 13, 8, 6, 13, 14, 15, 1, 20, 15, 13, 20, 0, 1, 8, 6, 1, 20, 6, 7, 8, 15, 13, 8, 6, 13, 14, 15, 1, 20, 15, 13, 20]

sage: [power_mod(n,3,22 )for n in xrange(0, 82)] #ok A070484    n^3 mod 22.

[0, 1, 8, 5, 20, 15, 18, 13, 6, 3, 10, 11, 12, 19, 16, 9, 4, 7, 2, 17, 14, 21, 0, 1, 8, 5, 20, 15, 18, 13, 6, 3, 10, 11, 12, 19, 16, 9, 4, 7, 2, 17, 14, 21, 0, 1, 8, 5, 20, 15, 18, 13, 6, 3, 10, 11, 12, 19, 16, 9, 4, 7, 2, 17, 14, 21, 0, 1, 8, 5, 20, 15, 18, 13, 6, 3, 10, 11, 12, 19, 16, 9]

sage: [power_mod(n,3,23 )for n in xrange(0, 82)] #ok A070485    n^3 mod 23.

[0, 1, 8, 4, 18, 10, 9, 21, 6, 16, 11, 20, 3, 12, 7, 17, 2, 14, 13, 5, 19, 15, 22, 0, 1, 8, 4, 18, 10, 9, 21, 6, 16, 11, 20, 3, 12, 7, 17, 2, 14, 13, 5, 19, 15, 22, 0, 1, 8, 4, 18, 10, 9, 21, 6, 16, 11, 20, 3, 12, 7, 17, 2, 14, 13, 5, 19, 15, 22, 0, 1, 8, 4, 18, 10, 9, 21, 6, 16, 11, 20, 3]

sage: [power_mod(n,3,24 )for n in xrange(0, 83)] #ok feljebbA070486    a(n) = n^3 mod 24 (or equivalently, n^5 mod 24).

[0, 1, 8, 3, 16, 5, 0, 7, 8, 9, 16, 11, 0, 13, 8, 15, 16, 17, 0, 19, 8, 21, 16, 23, 0, 1, 8, 3, 16, 5, 0, 7, 8, 9, 16, 11, 0, 13, 8, 15, 16, 17, 0, 19, 8, 21, 16, 23, 0, 1, 8, 3, 16, 5, 0, 7, 8, 9, 16, 11, 0, 13, 8, 15, 16, 17, 0, 19, 8, 21, 16, 23, 0, 1, 8, 3, 16, 5, 0, 7, 8, 9, 16]

sage: [power_mod(n,3,25 )for n in xrange(0, 85)] #ok A070487    n^3 mod 25.

[0, 1, 8, 2, 14, 0, 16, 18, 12, 4, 0, 6, 3, 22, 19, 0, 21, 13, 7, 9, 0, 11, 23, 17, 24, 0, 1, 8, 2, 14, 0, 16, 18, 12, 4, 0, 6, 3, 22, 19, 0, 21, 13, 7, 9, 0, 11, 23, 17, 24, 0, 1, 8, 2, 14, 0, 16, 18, 12, 4, 0, 6, 3, 22, 19, 0, 21, 13, 7, 9, 0, 11, 23, 17, 24, 0, 1, 8, 2, 14, 0, 16, 18, 12, 4]

sage: [power_mod(n,3,26 )for n in xrange(0, 81)] #OK A070488  	 n^3 mod 26.

[0, 1, 8, 1, 12, 21, 8, 5, 18, 1, 12, 5, 12, 13, 14, 21, 14, 25, 8, 21, 18, 5, 14, 25, 18, 25, 0, 1, 8, 1, 12, 21, 8, 5, 18, 1, 12, 5, 12, 13, 14, 21, 14, 25, 8, 21, 18, 5, 14, 25, 18, 25, 0, 1, 8, 1, 12, 21, 8, 5, 18, 1, 12, 5, 12, 13, 14, 21, 14, 25, 8, 21, 18, 5, 14, 25, 18, 25, 0, 1, 8]

sage: [power_mod(n,3,27 )for n in xrange(0, 86)] #ok A070489    n^3 mod 27.

[0, 1, 8, 0, 10, 17, 0, 19, 26, 0, 1, 8, 0, 10, 17, 0, 19, 26, 0, 1, 8, 0, 10, 17, 0, 19, 26, 0, 1, 8, 0, 10, 17, 0, 19, 26, 0, 1, 8, 0, 10, 17, 0, 19, 26, 0, 1, 8, 0, 10, 17, 0, 19, 26, 0, 1, 8, 0, 10, 17, 0, 19, 26, 0, 1, 8, 0, 10, 17, 0, 19, 26, 0, 1, 8, 0, 10, 17, 0, 19, 26, 0, 1, 8, 0, 10]

sage: [power_mod(n,3,28 )for n in xrange(0, 81)] #

[0, 1, 8, 27, 8, 13, 20, 7, 8, 1, 20, 15, 20, 13, 0, 15, 8, 13, 8, 27, 20, 21, 8, 15, 20, 1, 20, 27, 0, 1, 8, 27, 8, 13, 20, 7, 8, 1, 20, 15, 20, 13, 0, 15, 8, 13, 8, 27, 20, 21, 8, 15, 20, 1, 20, 27, 0, 1, 8, 27, 8, 13, 20, 7, 8, 1, 20, 15, 20, 13, 0, 15, 8, 13, 8, 27, 20, 21, 8, 15, 20]

sage: [power_mod(n,3,29 )for n in xrange(0, 78)] #ok A070491  	   n^3 mod 29.

[0, 1, 8, 27, 6, 9, 13, 24, 19, 4, 14, 26, 17, 22, 18, 11, 7, 12, 3, 15, 25, 10, 5, 16, 20, 23, 2, 21, 28, 0, 1, 8, 27, 6, 9, 13, 24, 19, 4, 14, 26, 17, 22, 18, 11, 7, 12, 3, 15, 25, 10, 5, 16, 20, 23, 2, 21, 28, 0, 1, 8, 27, 6, 9, 13, 24, 19, 4, 14, 26, 17, 22, 18, 11, 7, 12, 3, 15]

sage: [power_mod(n,3,30 )for n in xrange(0, 78)] #ok fentebb A070492  	  n^3 mod 30.

[0, 1, 8, 27, 4, 5, 6, 13, 2, 9, 10, 11, 18, 7, 14, 15, 16, 23, 12, 19, 20, 21, 28, 17, 24, 25, 26, 3, 22, 29, 0, 1, 8, 27, 4, 5, 6, 13, 2, 9, 10, 11, 18, 7, 14, 15, 16, 23, 12, 19, 20, 21, 28, 17, 24, 25, 26, 3, 22, 29, 0, 1, 8, 27, 4, 5, 6, 13, 2, 9, 10, 11, 18, 7, 14, 15, 16, 23]

sage: [power_mod(n,3,31 )for n in xrange(0, 81)] #okA070493   	 n^3 mod 31.

[0, 1, 8, 27, 2, 1, 30, 2, 16, 16, 8, 29, 23, 27, 16, 27, 4, 15, 4, 8, 2, 23, 15, 15, 29, 1, 30, 29, 4, 23, 30, 0, 1, 8, 27, 2, 1, 30, 2, 16, 16, 8, 29, 23, 27, 16, 27, 4, 15, 4, 8, 2, 23, 15, 15, 29, 1, 30, 29, 4, 23, 30, 0, 1, 8, 27, 2, 1, 30, 2, 16, 16, 8, 29, 23, 27, 16, 27, 4, 15, 4]

sage: [power_mod(n,3,32 )for n in xrange(0, 83)] #okA070494  	 	 n^3 mod 32.

[0, 1, 8, 27, 0, 29, 24, 23, 0, 25, 8, 19, 0, 21, 24, 15, 0, 17, 8, 11, 0, 13, 24, 7, 0, 9, 8, 3, 0, 5, 24, 31, 0, 1, 8, 27, 0, 29, 24, 23, 0, 25, 8, 19, 0, 21, 24, 15, 0, 17, 8, 11, 0, 13, 24, 7, 0, 9, 8, 3, 0, 5, 24, 31, 0, 1, 8, 27, 0, 29, 24, 23, 0, 25, 8, 19, 0, 21, 24, 15, 0, 17, 8]

sage: [power_mod(n,3,33 )for n in xrange(0, 76)] #

[0, 1, 8, 27, 31, 26, 18, 13, 17, 3, 10, 11, 12, 19, 5, 9, 4, 29, 24, 28, 14, 21, 22, 23, 30, 16, 20, 15, 7, 2, 6, 25, 32, 0, 1, 8, 27, 31, 26, 18, 13, 17, 3, 10, 11, 12, 19, 5, 9, 4, 29, 24, 28, 14, 21, 22, 23, 30, 16, 20, 15, 7, 2, 6, 25, 32, 0, 1, 8, 27, 31, 26, 18, 13, 17, 3]

sage: [power_mod(n,3,34 )for n in xrange(0,78)] #

[0, 1, 8, 27, 30, 23, 12, 3, 2, 15, 14, 5, 28, 21, 24, 9, 16, 17, 18, 25, 10, 13, 6, 29, 20, 19, 32, 31, 22, 11, 4, 7, 26, 33, 0, 1, 8, 27, 30, 23, 12, 3, 2, 15, 14, 5, 28, 21, 24, 9, 16, 17, 18, 25, 10, 13, 6, 29, 20, 19, 32, 31, 22, 11, 4, 7, 26, 33, 0, 1, 8, 27, 30, 23, 12, 3, 2, 15]

sage: [power_mod(n,3,35 )for n in xrange(0, 77)] #

[0, 1, 8, 27, 29, 20, 6, 28, 22, 29, 20, 1, 13, 27, 14, 15, 1, 13, 22, 34, 20, 21, 8, 22, 34, 15, 6, 13, 7, 29, 15, 6, 8, 27, 34, 0, 1, 8, 27, 29, 20, 6, 28, 22, 29, 20, 1, 13, 27, 14, 15, 1, 13, 22, 34, 20, 21, 8, 22, 34, 15, 6, 13, 7, 29, 15, 6, 8, 27, 34, 0, 1, 8, 27, 29, 20, 6]

sage: [power_mod(n,3,36 )for n in xrange(0, 83)] #ok

[0, 1, 8, 27, 28, 17, 0, 19, 8, 9, 28, 35, 0, 1, 8, 27, 28, 17, 0, 19, 8, 9, 28, 35, 0, 1, 8, 27, 28, 17, 0, 19, 8, 9, 28, 35, 0, 1, 8, 27, 28, 17, 0, 19, 8, 9, 28, 35, 0, 1, 8, 27, 28, 17, 0, 19, 8, 9, 28, 35, 0, 1, 8, 27, 28, 17, 0, 19, 8, 9, 28, 35, 0, 1, 8, 27, 28, 17, 0, 19, 8, 9, 28]

sage: [power_mod(n,3,37 )for n in xrange(0, 76)] #

[0, 1, 8, 27, 27, 14, 31, 10, 31, 26, 1, 36, 26, 14, 6, 8, 26, 29, 23, 14, 8, 11, 29, 31, 23, 11, 1, 36, 11, 6, 27, 6, 23, 10, 10, 29, 36, 0, 1, 8, 27, 27, 14, 31, 10, 31, 26, 1, 36, 26, 14, 6, 8, 26, 29, 23, 14, 8, 11, 29, 31, 23, 11, 1, 36, 11, 6, 27, 6, 23, 10, 10, 29, 36, 0, 1]

sage: [power_mod(n,3,38 )for n in xrange(0, 75)] #

[0, 1, 8, 27, 26, 11, 26, 1, 18, 7, 12, 1, 18, 31, 8, 31, 30, 11, 18, 19, 20, 27, 8, 7, 30, 7, 20, 37, 26, 31, 20, 37, 12, 27, 12, 11, 30, 37, 0, 1, 8, 27, 26, 11, 26, 1, 18, 7, 12, 1, 18, 31, 8, 31, 30, 11, 18, 19, 20, 27, 8, 7, 30, 7, 20, 37, 26, 31, 20, 37, 12, 27, 12, 11, 30]

sage: [power_mod(n,3,39 )for n in xrange(0, 75)] #

[0, 1, 8, 27, 25, 8, 21, 31, 5, 27, 25, 5, 12, 13, 14, 21, 1, 38, 21, 34, 5, 18, 1, 38, 18, 25, 26, 27, 34, 14, 12, 34, 8, 18, 31, 14, 12, 31, 38, 0, 1, 8, 27, 25, 8, 21, 31, 5, 27, 25, 5, 12, 13, 14, 21, 1, 38, 21, 34, 5, 18, 1, 38, 18, 25, 26, 27, 34, 14, 12, 34, 8, 18, 31, 14]

sage: [power_mod(n,3,40 )for n in xrange(0, 77)] #

[0, 1, 8, 27, 24, 5, 16, 23, 32, 9, 0, 11, 8, 37, 24, 15, 16, 33, 32, 19, 0, 21, 8, 7, 24, 25, 16, 3, 32, 29, 0, 31, 8, 17, 24, 35, 16, 13, 32, 39, 0, 1, 8, 27, 24, 5, 16, 23, 32, 9, 0, 11, 8, 37, 24, 15, 16, 33, 32, 19, 0, 21, 8, 7, 24, 25, 16, 3, 32, 29, 0, 31, 8, 17, 24, 35, 16]

sage: [power_mod(n,3,41 )for n in xrange(0, 76)] #

[0, 1, 8, 27, 23, 2, 11, 15, 20, 32, 16, 19, 6, 24, 38, 13, 37, 34, 10, 12, 5, 36, 29, 31, 7, 4, 28, 3, 17, 35, 22, 25, 9, 21, 26, 30, 39, 18, 14, 33, 40, 0, 1, 8, 27, 23, 2, 11, 15, 20, 32, 16, 19, 6, 24, 38, 13, 37, 34, 10, 12, 5, 36, 29, 31, 7, 4, 28, 3, 17, 35, 22, 25, 9, 21, 26]

sage: [power_mod(n,3,42 )for n in xrange(0, 76)] #

[0, 1, 8, 27, 22, 41, 6, 7, 8, 15, 34, 29, 6, 13, 14, 15, 22, 41, 36, 13, 20, 21, 22, 29, 6, 1, 20, 27, 28, 29, 36, 13, 8, 27, 34, 35, 36, 1, 20, 15, 34, 41, 0, 1, 8, 27, 22, 41, 6, 7, 8, 15, 34, 29, 6, 13, 14, 15, 22, 41, 36, 13, 20, 21, 22, 29, 6, 1, 20, 27, 28, 29, 36, 13, 8, 27]

sage: [power_mod(n,3,43 )for n in xrange(0, 76)] #

[0, 1, 8, 27, 21, 39, 1, 42, 39, 41, 11, 41, 8, 4, 35, 21, 11, 11, 27, 22, 2, 16, 27, 41, 21, 16, 32, 32, 22, 8, 39, 35, 2, 32, 2, 4, 1, 42, 4, 22, 16, 35, 42, 0, 1, 8, 27, 21, 39, 1, 42, 39, 41, 11, 41, 8, 4, 35, 21, 11, 11, 27, 22, 2, 16, 27, 41, 21, 16, 32, 32, 22, 8, 39, 35, 2]

sage: [power_mod(n,3,44 )for n in xrange(0, 76)] #

[0, 1, 8, 27, 20, 37, 40, 35, 28, 25, 32, 11, 12, 41, 16, 31, 4, 29, 24, 39, 36, 21, 0, 23, 8, 5, 20, 15, 40, 13, 28, 3, 32, 33, 12, 19, 16, 9, 4, 7, 24, 17, 36, 43, 0, 1, 8, 27, 20, 37, 40, 35, 28, 25, 32, 11, 12, 41, 16, 31, 4, 29, 24, 39, 36, 21, 0, 23, 8, 5, 20, 15, 40, 13, 28, 3]

sage: [power_mod(n,3,47 )for n in xrange(0, 74)] #ok 
A070509 		n^3 mod 47.

[0, 1, 8, 27, 17, 31, 28, 14, 42, 24, 13, 15, 36, 35, 18, 38, 7, 25, 4, 44, 10, 2, 26, 41, 6, 21, 45, 37, 3, 43, 22, 40, 9, 29, 12, 11, 32, 34, 23, 5, 33, 19, 16, 30, 20, 39, 46, 0, 1, 8, 27, 17, 31, 28, 14, 42, 24, 13, 15, 36, 35, 18, 38, 7, 25, 4, 44, 10, 2, 26, 41, 6, 21, 45]

sage: [power_mod(n,3,45 )for n in xrange(0, 76)] #ok A070507  	 	 n^3 mod 45.

[0, 1, 8, 27, 19, 35, 36, 28, 17, 9, 10, 26, 18, 37, 44, 0, 1, 8, 27, 19, 35, 36, 28, 17, 9, 10, 26, 18, 37, 44, 0, 1, 8, 27, 19, 35, 36, 28, 17, 9, 10, 26, 18, 37, 44, 0, 1, 8, 27, 19, 35, 36, 28, 17, 9, 10, 26, 18, 37, 44, 0, 1, 8, 27, 19, 35, 36, 28, 17, 9, 10, 26, 18, 37, 44, 0]

sage: [power_mod(n,3,46 )for n in xrange(0, 74)] #ok A070508    n^3 mod 46.

[0, 1, 8, 27, 18, 33, 32, 21, 6, 39, 34, 43, 26, 35, 30, 17, 2, 37, 36, 5, 42, 15, 22, 23, 24, 31, 4, 41, 10, 9, 44, 29, 16, 11, 20, 3, 12, 7, 40, 25, 14, 13, 28, 19, 38, 45, 0, 1, 8, 27, 18, 33, 32, 21, 6, 39, 34, 43, 26, 35, 30, 17, 2, 37, 36, 5, 42, 15, 22, 23, 24, 31, 4, 41]

sage: [power_mod(n,3,48 )for n in xrange(0, 78)] #ok A070510  	  n^3 mod 48.

[0, 1, 8, 27, 16, 29, 24, 7, 32, 9, 40, 35, 0, 37, 8, 15, 16, 17, 24, 43, 32, 45, 40, 23, 0, 25, 8, 3, 16, 5, 24, 31, 32, 33, 40, 11, 0, 13, 8, 39, 16, 41, 24, 19, 32, 21, 40, 47, 0, 1, 8, 27, 16, 29, 24, 7, 32, 9, 40, 35, 0, 37, 8, 15, 16, 17, 24, 43, 32, 45, 40, 23, 0, 25, 8, 3, 16, 5]

sage: [power_mod(n,4,1 )for n in xrange(0, 83)] #nnn

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

sage: [power_mod(n,4,2 )for n in xrange(0, 83)] #nnn

[0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]

sage: [power_mod(n,4,3)for n in xrange(0, 83)] #nnn

[0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1]

sage: [power_mod(n,4,4)for n in xrange(0, 83)] #nnn

[0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]

sage: [power_mod(n,4,5)for n in xrange(0, 83)] #nnnn

[0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1]

sage: [power_mod(n,2,6)for n in xrange(0, 101)] #ok A070431    n^2 mod 6. A070511  	 	 n^4 mod 6.

[0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4]

sage: [power_mod(n,4,6)for n in xrange(0, 98)] #okA070511    n^4 mod 6.

[0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1, 4, 3, 4, 1, 0, 1]

sage: [power_mod(n,4,7)for n in xrange(0, 101)] #okA070512  	  n^4 mod 7.

[0, 1, 2, 4, 4, 2, 1, 0, 1, 2, 4, 4, 2, 1, 0, 1, 2, 4, 4, 2, 1, 0, 1, 2, 4, 4, 2, 1, 0, 1, 2, 4, 4, 2, 1, 0, 1, 2, 4, 4, 2, 1, 0, 1, 2, 4, 4, 2, 1, 0, 1, 2, 4, 4, 2, 1, 0, 1, 2, 4, 4, 2, 1, 0, 1, 2, 4, 4, 2, 1, 0, 1, 2, 4, 4, 2, 1, 0, 1, 2, 4, 4, 2, 1, 0, 1, 2, 4, 4, 2, 1, 0, 1, 2, 4, 4, 2, 1, 0, 1, 2]

sage: [power_mod(n,4,8)for n in xrange(0, 83)] #nnnnnnnnnnnnnnnnn

[0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]

sage: [power_mod(n,4,9)for n in xrange(0, 101)] #okA070513    n^4 mod 9.

[0, 1, 7, 0, 4, 4, 0, 7, 1, 0, 1, 7, 0, 4, 4, 0, 7, 1, 0, 1, 7, 0, 4, 4, 0, 7, 1, 0, 1, 7, 0, 4, 4, 0, 7, 1, 0, 1, 7, 0, 4, 4, 0, 7, 1, 0, 1, 7, 0, 4, 4, 0, 7, 1, 0, 1, 7, 0, 4, 4, 0, 7, 1, 0, 1, 7, 0, 4, 4, 0, 7, 1, 0, 1, 7, 0, 4, 4, 0, 7, 1, 0, 1, 7, 0, 4, 4, 0, 7, 1, 0, 1, 7, 0, 4, 4, 0, 7, 1, 0, 1]

sage: [power_mod(n,4,10)for n in xrange(0, 101)] #okA070514    n^4 mod 10.

[0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0]

sage: [power_mod(n,4,11)for n in xrange(0, 101)] #ok A070515  n^4 mod 11.

[0, 1, 5, 4, 3, 9, 9, 3, 4, 5, 1, 0, 1, 5, 4, 3, 9, 9, 3, 4, 5, 1, 0, 1, 5, 4, 3, 9, 9, 3, 4, 5, 1, 0, 1, 5, 4, 3, 9, 9, 3, 4, 5, 1, 0, 1, 5, 4, 3, 9, 9, 3, 4, 5, 1, 0, 1, 5, 4, 3, 9, 9, 3, 4, 5, 1, 0, 1, 5, 4, 3, 9, 9, 3, 4, 5, 1, 0, 1, 5, 4, 3, 9, 9, 3, 4, 5, 1, 0, 1, 5, 4, 3, 9, 9, 3, 4, 5, 1, 0, 1]

sage: [power_mod(n,4,12)for n in xrange(0, 101)] #ok A070435  	  n^2 mod 12. equ

[0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4]

sage: [power_mod(n,4,13)for n in xrange(0, 101)] #ok A070517  	  n^4 mod 13.

[0, 1, 3, 3, 9, 1, 9, 9, 1, 9, 3, 3, 1, 0, 1, 3, 3, 9, 1, 9, 9, 1, 9, 3, 3, 1, 0, 1, 3, 3, 9, 1, 9, 9, 1, 9, 3, 3, 1, 0, 1, 3, 3, 9, 1, 9, 9, 1, 9, 3, 3, 1, 0, 1, 3, 3, 9, 1, 9, 9, 1, 9, 3, 3, 1, 0, 1, 3, 3, 9, 1, 9, 9, 1, 9, 3, 3, 1, 0, 1, 3, 3, 9, 1, 9, 9, 1, 9, 3, 3, 1, 0, 1, 3, 3, 9, 1, 9, 9, 1, 9]

sage: [power_mod(n,4,14)for n in xrange(0, 97)] #ok A070532  	  n^4 mod 14.

[0, 1, 2, 11, 4, 9, 8, 7, 8, 9, 4, 11, 2, 1, 0, 1, 2, 11, 4, 9, 8, 7, 8, 9, 4, 11, 2, 1, 0, 1, 2, 11, 4, 9, 8, 7, 8, 9, 4, 11, 2, 1, 0, 1, 2, 11, 4, 9, 8, 7, 8, 9, 4, 11, 2, 1, 0, 1, 2, 11, 4, 9, 8, 7, 8, 9, 4, 11, 2, 1, 0, 1, 2, 11, 4, 9, 8, 7, 8, 9, 4, 11, 2, 1, 0, 1, 2, 11, 4, 9, 8, 7, 8, 9, 4, 11, 2]

sage: [power_mod(n,4,15)for n in xrange(0, 97)] #ok A070533  	  n^4 mod 15.

[0, 1, 1, 6, 1, 10, 6, 1, 1, 6, 10, 1, 6, 1, 1, 0, 1, 1, 6, 1, 10, 6, 1, 1, 6, 10, 1, 6, 1, 1, 0, 1, 1, 6, 1, 10, 6, 1, 1, 6, 10, 1, 6, 1, 1, 0, 1, 1, 6, 1, 10, 6, 1, 1, 6, 10, 1, 6, 1, 1, 0, 1, 1, 6, 1, 10, 6, 1, 1, 6, 10, 1, 6, 1, 1, 0, 1, 1, 6, 1, 10, 6, 1, 1, 6, 10, 1, 6, 1, 1, 0, 1, 1, 6, 1, 10, 6]

sage: [power_mod(n,4,16)for n in xrange(0, 101)] #nnnnnnnnnnnnnnn

[0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]

sage: [power_mod(n,4,17)for n in xrange(0, 84)] #ok A070534 	 n^4 mod 17.

[0, 1, 16, 13, 1, 13, 4, 4, 16, 16, 4, 4, 13, 1, 13, 16, 1, 0, 1, 16, 13, 1, 13, 4, 4, 16, 16, 4, 4, 13, 1, 13, 16, 1, 0, 1, 16, 13, 1, 13, 4, 4, 16, 16, 4, 4, 13, 1, 13, 16, 1, 0, 1, 16, 13, 1, 13, 4, 4, 16, 16, 4, 4, 13, 1, 13, 16, 1, 0, 1, 16, 13, 1, 13, 4, 4, 16, 16, 4, 4, 13, 1, 13, 16]

sage: [power_mod(n,4,18)for n in xrange(0, 90)] #ok A070535   	 n^4 mod 18.

[0, 1, 16, 9, 4, 13, 0, 7, 10, 9, 10, 7, 0, 13, 4, 9, 16, 1, 0, 1, 16, 9, 4, 13, 0, 7, 10, 9, 10, 7, 0, 13, 4, 9, 16, 1, 0, 1, 16, 9, 4, 13, 0, 7, 10, 9, 10, 7, 0, 13, 4, 9, 16, 1, 0, 1, 16, 9, 4, 13, 0, 7, 10, 9, 10, 7, 0, 13, 4, 9, 16, 1, 0, 1, 16, 9, 4, 13, 0, 7, 10, 9, 10, 7, 0, 13, 4, 9, 16, 1]

sage: [power_mod(n,4,19)for n in xrange(0, 90)] #ok A070538   	 n^4 mod 19.

[0, 1, 16, 5, 9, 17, 4, 7, 11, 6, 6, 11, 7, 4, 17, 9, 5, 16, 1, 0, 1, 16, 5, 9, 17, 4, 7, 11, 6, 6, 11, 7, 4, 17, 9, 5, 16, 1, 0, 1, 16, 5, 9, 17, 4, 7, 11, 6, 6, 11, 7, 4, 17, 9, 5, 16, 1, 0, 1, 16, 5, 9, 17, 4, 7, 11, 6, 6, 11, 7, 4, 17, 9, 5, 16, 1, 0, 1, 16, 5, 9, 17, 4, 7, 11, 6, 6, 11, 7, 4]

sage: [power_mod(n,4,5 )*power_mod(n,4,6 )for n in xrange(0, 87)] #nnnn

[0, 1, 4, 3, 4, 0, 0, 1, 4, 3, 0, 1, 0, 1, 4, 0, 4, 1, 0, 1, 0, 3, 4, 1, 0, 0, 4, 3, 4, 1, 0, 1, 4, 3, 4, 0, 0, 1, 4, 3, 0, 1, 0, 1, 4, 0, 4, 1, 0, 1, 0, 3, 4, 1, 0, 0, 4, 3, 4, 1, 0, 1, 4, 3, 4, 0, 0, 1, 4, 3, 0, 1, 0, 1, 4, 0, 4, 1, 0, 1, 0, 3, 4, 1, 0, 0, 4]

sage: [power_mod(n,4,20)for n in xrange(0, 87)] #ok A070539    n^4 mod 20.

[0, 1, 16, 1, 16, 5, 16, 1, 16, 1, 0, 1, 16, 1, 16, 5, 16, 1, 16, 1, 0, 1, 16, 1, 16, 5, 16, 1, 16, 1, 0, 1, 16, 1, 16, 5, 16, 1, 16, 1, 0, 1, 16, 1, 16, 5, 16, 1, 16, 1, 0, 1, 16, 1, 16, 5, 16, 1, 16, 1, 0, 1, 16, 1, 16, 5, 16, 1, 16, 1, 0, 1, 16, 1, 16, 5, 16, 1, 16, 1, 0, 1, 16, 1, 16, 5, 16]

sage: [power_mod(n,4,21)for n in xrange(0, 88)] #ok A070540  	 	 n^4 mod 21.

[0, 1, 16, 18, 4, 16, 15, 7, 1, 9, 4, 4, 9, 1, 7, 15, 16, 4, 18, 16, 1, 0, 1, 16, 18, 4, 16, 15, 7, 1, 9, 4, 4, 9, 1, 7, 15, 16, 4, 18, 16, 1, 0, 1, 16, 18, 4, 16, 15, 7, 1, 9, 4, 4, 9, 1, 7, 15, 16, 4, 18, 16, 1, 0, 1, 16, 18, 4, 16, 15, 7, 1, 9, 4, 4, 9, 1, 7, 15, 16, 4, 18, 16, 1, 0, 1, 16, 18]

sage: [power_mod(n,4,22)for n in xrange(0, 84)] #ok A070541   n^4 mod 22.

[0, 1, 16, 15, 14, 9, 20, 3, 4, 5, 12, 11, 12, 5, 4, 3, 20, 9, 14, 15, 16, 1, 0, 1, 16, 15, 14, 9, 20, 3, 4, 5, 12, 11, 12, 5, 4, 3, 20, 9, 14, 15, 16, 1, 0, 1, 16, 15, 14, 9, 20, 3, 4, 5, 12, 11, 12, 5, 4, 3, 20, 9, 14, 15, 16, 1, 0, 1, 16, 15, 14, 9, 20, 3, 4, 5, 12, 11, 12, 5, 4, 3, 20, 9]

sage: [power_mod(n,4,23)for n in xrange(0, 89)] #ok A070551  	  n^4 mod 23.

[0, 1, 16, 12, 3, 4, 8, 9, 2, 6, 18, 13, 13, 18, 6, 2, 9, 8, 4, 3, 12, 16, 1, 0, 1, 16, 12, 3, 4, 8, 9, 2, 6, 18, 13, 13, 18, 6, 2, 9, 8, 4, 3, 12, 16, 1, 0, 1, 16, 12, 3, 4, 8, 9, 2, 6, 18, 13, 13, 18, 6, 2, 9, 8, 4, 3, 12, 16, 1, 0, 1, 16, 12, 3, 4, 8, 9, 2, 6, 18, 13, 13, 18, 6, 2, 9, 8, 4, 3]

sage: [power_mod(n,4,24)for n in xrange(0, 90)] #ok A070567  n^4 mod 24.

[0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1, 0, 1, 16, 9, 16, 1]

sage: [power_mod(n,4,25)for n in xrange(0, 84)] #ok A070568    n^4 mod 25.

[0, 1, 16, 6, 6, 0, 21, 1, 21, 11, 0, 16, 11, 11, 16, 0, 11, 21, 1, 21, 0, 6, 6, 16, 1, 0, 1, 16, 6, 6, 0, 21, 1, 21, 11, 0, 16, 11, 11, 16, 0, 11, 21, 1, 21, 0, 6, 6, 16, 1, 0, 1, 16, 6, 6, 0, 21, 1, 21, 11, 0, 16, 11, 11, 16, 0, 11, 21, 1, 21, 0, 6, 6, 16, 1, 0, 1, 16, 6, 6, 0, 21, 1, 21]

sage: [power_mod(n,4,26)for n in xrange(0, 84)] # ok A070569  	  n^4 mod 26.

[0, 1, 16, 3, 22, 1, 22, 9, 14, 9, 16, 3, 14, 13, 14, 3, 16, 9, 14, 9, 22, 1, 22, 3, 16, 1, 0, 1, 16, 3, 22, 1, 22, 9, 14, 9, 16, 3, 14, 13, 14, 3, 16, 9, 14, 9, 22, 1, 22, 3, 16, 1, 0, 1, 16, 3, 22, 1, 22, 9, 14, 9, 16, 3, 14, 13, 14, 3, 16, 9, 14, 9, 22, 1, 22, 3, 16, 1, 0, 1, 16, 3, 22, 1]

sage: [power_mod(n,4,27)for n in xrange(0, 84)] #ok A070570    n^4 mod 27.

[0, 1, 16, 0, 13, 4, 0, 25, 19, 0, 10, 7, 0, 22, 22, 0, 7, 10, 0, 19, 25, 0, 4, 13, 0, 16, 1, 0, 1, 16, 0, 13, 4, 0, 25, 19, 0, 10, 7, 0, 22, 22, 0, 7, 10, 0, 19, 25, 0, 4, 13, 0, 16, 1, 0, 1, 16, 0, 13, 4, 0, 25, 19, 0, 10, 7, 0, 22, 22, 0, 7, 10, 0, 19, 25, 0, 4, 13, 0, 16, 1, 0, 1, 16]

sage: [power_mod(n,4,28)for n in xrange(0, 88)] #okA070571    n^4 mod 28.

[0, 1, 16, 25, 4, 9, 8, 21, 8, 9, 4, 25, 16, 1, 0, 1, 16, 25, 4, 9, 8, 21, 8, 9, 4, 25, 16, 1, 0, 1, 16, 25, 4, 9, 8, 21, 8, 9, 4, 25, 16, 1, 0, 1, 16, 25, 4, 9, 8, 21, 8, 9, 4, 25, 16, 1, 0, 1, 16, 25, 4, 9, 8, 21, 8, 9, 4, 25, 16, 1, 0, 1, 16, 25, 4, 9, 8, 21, 8, 9, 4, 25, 16, 1, 0, 1, 16, 25]

sage: [power_mod(n,4,29)for n in xrange(0, 77)] # okA070572  n^4 mod 29.

[0, 1, 16, 23, 24, 16, 20, 23, 7, 7, 24, 25, 1, 25, 20, 20, 25, 1, 25, 24, 7, 7, 23, 20, 16, 24, 23, 16, 1, 0, 1, 16, 23, 24, 16, 20, 23, 7, 7, 24, 25, 1, 25, 20, 20, 25, 1, 25, 24, 7, 7, 23, 20, 16, 24, 23, 16, 1, 0, 1, 16, 23, 24, 16, 20, 23, 7, 7, 24, 25, 1, 25, 20, 20, 25, 1, 25]

sage: [power_mod(n,4,30)for n in xrange(0, 81)] #ok A070573    n^4 mod 30.

[0, 1, 16, 21, 16, 25, 6, 1, 16, 21, 10, 1, 6, 1, 16, 15, 16, 1, 6, 1, 10, 21, 16, 1, 6, 25, 16, 21, 16, 1, 0, 1, 16, 21, 16, 25, 6, 1, 16, 21, 10, 1, 6, 1, 16, 15, 16, 1, 6, 1, 10, 21, 16, 1, 6, 25, 16, 21, 16, 1, 0, 1, 16, 21, 16, 25, 6, 1, 16, 21, 10, 1, 6, 1, 16, 15, 16, 1, 6, 1, 10]

sage: [power_mod(n,4,31)for n in xrange(0, 83)] #ok A070574    n^4 mod 31.

[0, 1, 16, 19, 8, 5, 25, 14, 4, 20, 18, 9, 28, 10, 7, 2, 2, 7, 10, 28, 9, 18, 20, 4, 14, 25, 5, 8, 19, 16, 1, 0, 1, 16, 19, 8, 5, 25, 14, 4, 20, 18, 9, 28, 10, 7, 2, 2, 7, 10, 28, 9, 18, 20, 4, 14, 25, 5, 8, 19, 16, 1, 0, 1, 16, 19, 8, 5, 25, 14, 4, 20, 18, 9, 28, 10, 7, 2, 2, 7, 10, 28, 9]

sage: [power_mod(n,4,32)for n in xrange(0, 84)] #ok A070575   n^4 mod 32.

[0, 1, 16, 17, 0, 17, 16, 1, 0, 1, 16, 17, 0, 17, 16, 1, 0, 1, 16, 17, 0, 17, 16, 1, 0, 1, 16, 17, 0, 17, 16, 1, 0, 1, 16, 17, 0, 17, 16, 1, 0, 1, 16, 17, 0, 17, 16, 1, 0, 1, 16, 17, 0, 17, 16, 1, 0, 1, 16, 17, 0, 17, 16, 1, 0, 1, 16, 17, 0, 17, 16, 1, 0, 1, 16, 17, 0, 17, 16, 1, 0, 1, 16, 17]

sage: [power_mod(n,4,33)for n in xrange(0, 80)] #ok A070576   n^4 mod 33.

[0, 1, 16, 15, 25, 31, 9, 25, 4, 27, 1, 22, 12, 16, 4, 3, 31, 31, 3, 4, 16, 12, 22, 1, 27, 4, 25, 9, 31, 25, 15, 16, 1, 0, 1, 16, 15, 25, 31, 9, 25, 4, 27, 1, 22, 12, 16, 4, 3, 31, 31, 3, 4, 16, 12, 22, 1, 27, 4, 25, 9, 31, 25, 15, 16, 1, 0, 1, 16, 15, 25, 31, 9, 25, 4, 27, 1, 22, 12, 16]

sage: [power_mod(n,4,34)for n in xrange(0, 75)] # ok A070577     n^4 mod 34.

[0, 1, 16, 13, 18, 13, 4, 21, 16, 33, 4, 21, 30, 1, 30, 33, 18, 17, 18, 33, 30, 1, 30, 21, 4, 33, 16, 21, 4, 13, 18, 13, 16, 1, 0, 1, 16, 13, 18, 13, 4, 21, 16, 33, 4, 21, 30, 1, 30, 33, 18, 17, 18, 33, 30, 1, 30, 21, 4, 33, 16, 21, 4, 13, 18, 13, 16, 1, 0, 1, 16, 13, 18, 13, 4]

sage: [power_mod(n,5,30)for n in xrange(0, 75)] #nem kell

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]

sage: [power_mod(n,6,30)for n in xrange(0, 75)]#A070653 n^6mod30.és A070452          n^2 mod 30.

[0, 1, 4, 9, 16, 25, 6, 19, 4, 21, 10, 1, 24, 19, 16, 15, 16, 19, 24, 1, 10, 21, 4, 19, 6, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 6, 19, 4, 21, 10, 1, 24, 19, 16, 15, 16, 19, 24, 1, 10, 21, 4, 19, 6, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 6, 19, 4, 21, 10, 1, 24, 19, 16]

sage: [power_mod(n,7,30)for n in xrange(0, 75)] #

[0, 1, 8, 27, 4, 5, 6, 13, 2, 9, 10, 11, 18, 7, 14, 15, 16, 23, 12, 19, 20, 21, 28, 17, 24, 25, 26, 3, 22, 29, 0, 1, 8, 27, 4, 5, 6, 13, 2, 9, 10, 11, 18, 7, 14, 15, 16, 23, 12, 19, 20, 21, 28, 17, 24, 25, 26, 3, 22, 29, 0, 1, 8, 27, 4, 5, 6, 13, 2, 9, 10, 11, 18, 7, 14]

sage: [power_mod(n,8,30)for n in xrange(0, 75)] # mi legyen? A070573  	  n^4 mod 30.

[0, 1, 16, 21, 16, 25, 6, 1, 16, 21, 10, 1, 6, 1, 16, 15, 16, 1, 6, 1, 10, 21, 16, 1, 6, 25, 16, 21, 16, 1, 0, 1, 16, 21, 16, 25, 6, 1, 16, 21, 10, 1, 6, 1, 16, 15, 16, 1, 6, 1, 10, 21, 16, 1, 6, 25, 16, 21, 16, 1, 0, 1, 16, 21, 16, 25, 6, 1, 16, 21, 10, 1, 6, 1, 16]

sage: [power_mod(n,9,20)for n in xrange(0, 75)] #újnak "n^9 mod 20" és equivalenty A070604    n^5 mod 20.

[0, 1, 12, 3, 4, 5, 16, 7, 8, 9, 0, 11, 12, 13, 4, 15, 16, 17, 8, 19, 0, 1, 12, 3, 4, 5, 16, 7, 8, 9, 0, 11, 12, 13, 4, 15, 16, 17, 8, 19, 0, 1, 12, 3, 4, 5, 16, 7, 8, 9, 0, 11, 12, 13, 4, 15, 16, 17, 8, 19, 0, 1, 12, 3, 4, 5, 16, 7, 8, 9, 0, 11, 12, 13, 4]

sage: [power_mod(n,9,30)for n in xrange(0, 75)] #nincs, újnak!

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]

sage: [power_mod(n,10,20)for n in xrange(0, 88)] #A070442    n^2 mod 20. equ

[0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9]

sage: [power_mod(n,11,30)for n in xrange(0, 78)] #Újnak és equivalenty !!!A070492    n^3 mod 30 A070711    n^7 mod 30.

[0, 1, 8, 27, 4, 5, 6, 13, 2, 9, 10, 11, 18, 7, 14, 15, 16, 23, 12, 19, 20, 21, 28, 17, 24, 25, 26, 3, 22, 29, 0, 1, 8, 27, 4, 5, 6, 13, 2, 9, 10, 11, 18, 7, 14, 15, 16, 23, 12, 19, 20, 21, 28, 17, 24, 25, 26, 3, 22, 29, 0, 1, 8, 27, 4, 5, 6, 13, 2, 9, 10, 11, 18, 7, 14, 15, 16, 23]

sage: [power_mod(n,13,17)for n in xrange(0, 78)] #nnnnnnnnnnnnnnnnnnnnnnnnn

[0, 1, 15, 12, 4, 3, 10, 6, 9, 8, 11, 7, 14, 13, 5, 2, 16, 0, 1, 15, 12, 4, 3, 10, 6, 9, 8, 11, 7, 14, 13, 5, 2, 16, 0, 1, 15, 12, 4, 3, 10, 6, 9, 8, 11, 7, 14, 13, 5, 2, 16, 0, 1, 15, 12, 4, 3, 10, 6, 9, 8, 11, 7, 14, 13, 5, 2, 16, 0, 1, 15, 12, 4, 3, 10, 6, 9, 8]

sage: [power_mod(n,13,30)for n in xrange(0, 78)] #nnnnnnnnnnn

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]

sage: [power_mod(n,8,21)for n in xrange(0, 99)] #nincs

[0, 1, 4, 9, 16, 4, 15, 7, 1, 18, 16, 16, 18, 1, 7, 15, 4, 16, 9, 4, 1, 0, 1, 4, 9, 16, 4, 15, 7, 1, 18, 16, 16, 18, 1, 7, 15, 4, 16, 9, 4, 1, 0, 1, 4, 9, 16, 4, 15, 7, 1, 18, 16, 16, 18, 1, 7, 15, 4, 16, 9, 4, 1, 0, 1, 4, 9, 16, 4, 15, 7, 1, 18, 16, 16, 18, 1, 7, 15, 4, 16, 9, 4, 1, 0, 1, 4, 9, 16, 4, 15, 7, 1, 18, 16, 16, 18, 1, 7]

sage: [power_mod(n,8,22)for n in xrange(0, 99)] #nincs

[0, 1, 14, 5, 20, 15, 4, 9, 16, 3, 12, 11, 12, 3, 16, 9, 4, 15, 20, 5, 14, 1, 0, 1, 14, 5, 20, 15, 4, 9, 16, 3, 12, 11, 12, 3, 16, 9, 4, 15, 20, 5, 14, 1, 0, 1, 14, 5, 20, 15, 4, 9, 16, 3, 12, 11, 12, 3, 16, 9, 4, 15, 20, 5, 14, 1, 0, 1, 14, 5, 20, 15, 4, 9, 16, 3, 12, 11, 12, 3, 16, 9, 4, 15, 20, 5, 14, 1, 0, 1, 14, 5, 20, 15, 4, 9, 16, 3, 12]

sage: [power_mod(n,8,23)for n in xrange(0, 99)] #nincs

[0, 1, 3, 6, 9, 16, 18, 12, 4, 13, 2, 8, 8, 2, 13, 4, 12, 18, 16, 9, 6, 3, 1, 0, 1, 3, 6, 9, 16, 18, 12, 4, 13, 2, 8, 8, 2, 13, 4, 12, 18, 16, 9, 6, 3, 1, 0, 1, 3, 6, 9, 16, 18, 12, 4, 13, 2, 8, 8, 2, 13, 4, 12, 18, 16, 9, 6, 3, 1, 0, 1, 3, 6, 9, 16, 18, 12, 4, 13, 2, 8, 8, 2, 13, 4, 12, 18, 16, 9, 6, 3, 1, 0, 1, 3, 6, 9, 16, 18]

sage: [lcm(n,1)for n in xrange(0, 22)] #

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]

sage: [lcm(n,2)for n in xrange(0, 68)] #ok A109043  	 	 LCM(n,2).

[0, 2, 2, 6, 4, 10, 6, 14, 8, 18, 10, 22, 12, 26, 14, 30, 16, 34, 18, 38, 20, 42, 22, 46, 24, 50, 26, 54, 28, 58, 30, 62, 32, 66, 34, 70, 36, 74, 38, 78, 40, 82, 42, 86, 44, 90, 46, 94, 48, 98, 50, 102, 52, 106, 54, 110, 56, 114, 58, 118, 60, 122, 62, 126, 64, 130, 66, 134]

sage: [lcm(n,2)/2for n in xrange(0, 77)] #ok A026741  	 	 a(n) = n if n odd, n/2 if n even.

[0, 1, 1, 3, 2, 5, 3, 7, 4, 9, 5, 11, 6, 13, 7, 15, 8, 17, 9, 19, 10, 21, 11, 23, 12, 25, 13, 27, 14, 29, 15, 31, 16, 33, 17, 35, 18, 37, 19, 39, 20, 41, 21, 43, 22, 45, 23, 47, 24, 49, 25, 51, 26, 53, 27, 55, 28, 57, 29, 59, 30, 61, 31, 63, 32, 65, 33, 67, 34, 69, 35, 71, 36, 73, 37, 75, 38]

sage: [lcm(n,3)for n in xrange(0, 64)] #ok A109044  LCM(n,3).

[0, 3, 6, 3, 12, 15, 6, 21, 24, 9, 30, 33, 12, 39, 42, 15, 48, 51, 18, 57, 60, 21, 66, 69, 24, 75, 78, 27, 84, 87, 30, 93, 96, 33, 102, 105, 36, 111, 114, 39, 120, 123, 42, 129, 132, 45, 138, 141, 48, 147, 150, 51, 156, 159, 54, 165, 168, 57, 174, 177, 60, 183, 186, 63]

sage: [lcm(n,4)for n in xrange(0, 63)] #

[0, 4, 4, 12, 4, 20, 12, 28, 8, 36, 20, 44, 12, 52, 28, 60, 16, 68, 36, 76, 20, 84, 44, 92, 24, 100, 52, 108, 28, 116, 60, 124, 32, 132, 68, 140, 36, 148, 76, 156, 40, 164, 84, 172, 44, 180, 92, 188, 48, 196, 100, 204, 52, 212, 108, 220, 56, 228, 116, 236, 60, 244, 124]

sage: [lcm(n,4)/2for n in xrange(0, 23)] #nnnnnnnnnnn

[0, 2, 2, 6, 2, 10, 6, 14, 4, 18, 10, 22, 6, 26, 14, 30, 8, 34, 18, 38, 10, 42, 22]

sage: [lcm(n,4)/4for n in xrange(1, 77)] #ok A060819  	 	 a(n) = n / gcd(n,4).

[1, 1, 3, 1, 5, 3, 7, 2, 9, 5, 11, 3, 13, 7, 15, 4, 17, 9, 19, 5, 21, 11, 23, 6, 25, 13, 27, 7, 29, 15, 31, 8, 33, 17, 35, 9, 37, 19, 39, 10, 41, 21, 43, 11, 45, 23, 47, 12, 49, 25, 51, 13, 53, 27, 55, 14, 57, 29, 59, 15, 61, 31, 63, 16, 65, 33, 67, 17, 69, 35, 71, 18, 73, 37, 75, 19]

sage: [lcm(n,5)for n in xrange(0, 59)] #ok A109046  	 
 	 LCM(n,5).

[0, 5, 10, 15, 20, 5, 30, 35, 40, 45, 10, 55, 60, 65, 70, 15, 80, 85, 90, 95, 20, 105, 110, 115, 120, 25, 130, 135, 140, 145, 30, 155, 160, 165, 170, 35, 180, 185, 190, 195, 40, 205, 210, 215, 220, 45, 230, 235, 240, 245, 50, 255, 260, 265, 270, 55, 280, 285, 290]

sage: [lcm(n,5)/5for n in xrange(1, 51)] #ok A060791  	 	 a(n) = n / GCD(n,5).

[1, 2, 3, 4, 1, 6, 7, 8, 9, 2, 11, 12, 13, 14, 3, 16, 17, 18, 19, 4, 21, 22, 23, 24, 5, 26, 27, 28, 29, 6, 31, 32, 33, 34, 7, 36, 37, 38, 39, 8, 41, 42, 43, 44, 9, 46, 47, 48, 49, 10]

sage: [lcm(n,6)for n in xrange(0, 60)] #ok A109047  	 	 LCM(n,6).

[0, 6, 6, 6, 12, 30, 6, 42, 24, 18, 30, 66, 12, 78, 42, 30, 48, 102, 18, 114, 60, 42, 66, 138, 24, 150, 78, 54, 84, 174, 30, 186, 96, 66, 102, 210, 36, 222, 114, 78, 120, 246, 42, 258, 132, 90, 138, 282, 48, 294, 150, 102, 156, 318, 54, 330, 168, 114, 174, 354]

sage: [lcm(n,6)/6for n in xrange(1, 78)] #ok A060789  	 	 a(n) = n / (gcd(n,2) * gcd(n,3)).

[1, 1, 1, 2, 5, 1, 7, 4, 3, 5, 11, 2, 13, 7, 5, 8, 17, 3, 19, 10, 7, 11, 23, 4, 25, 13, 9, 14, 29, 5, 31, 16, 11, 17, 35, 6, 37, 19, 13, 20, 41, 7, 43, 22, 15, 23, 47, 8, 49, 25, 17, 26, 53, 9, 55, 28, 19, 29, 59, 10, 61, 31, 21, 32, 65, 11, 67, 34, 23, 35, 71, 12, 73, 37, 25, 38, 77]

sage: [lcm(n,7)for n in xrange(0, 57)] #ok A109048  	 	 LCM(n,7).

[0, 7, 14, 21, 28, 35, 42, 7, 56, 63, 70, 77, 84, 91, 14, 105, 112, 119, 126, 133, 140, 21, 154, 161, 168, 175, 182, 189, 28, 203, 210, 217, 224, 231, 238, 35, 252, 259, 266, 273, 280, 287, 42, 301, 308, 315, 322, 329, 336, 49, 350, 357, 364, 371, 378, 385, 56]

sage: [lcm(n,7)/7for n in xrange(0, 77)] #ok A106608  	 	 Numerator of n/(n+7).

[0, 1, 2, 3, 4, 5, 6, 1, 8, 9, 10, 11, 12, 13, 2, 15, 16, 17, 18, 19, 20, 3, 22, 23, 24, 25, 26, 27, 4, 29, 30, 31, 32, 33, 34, 5, 36, 37, 38, 39, 40, 41, 6, 43, 44, 45, 46, 47, 48, 7, 50, 51, 52, 53, 54, 55, 8, 57, 58, 59, 60, 61, 62, 9, 64, 65, 66, 67, 68, 69, 10, 71, 72, 73, 74, 75, 76]

sage: [lcm(n,8)for n in xrange(0, 59)] #ok A109049  	 	 LCM(n,8).

[0, 8, 8, 24, 8, 40, 24, 56, 8, 72, 40, 88, 24, 104, 56, 120, 16, 136, 72, 152, 40, 168, 88, 184, 24, 200, 104, 216, 56, 232, 120, 248, 32, 264, 136, 280, 72, 296, 152, 312, 40, 328, 168, 344, 88, 360, 184, 376, 48, 392, 200, 408, 104, 424, 216, 440, 56, 456, 232]

sage: [lcm(n,8)/8for n in xrange(0, 80)] #ok A106609  	 	 Numerator of n/(n+8).

[0, 1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 2, 17, 9, 19, 5, 21, 11, 23, 3, 25, 13, 27, 7, 29, 15, 31, 4, 33, 17, 35, 9, 37, 19, 39, 5, 41, 21, 43, 11, 45, 23, 47, 6, 49, 25, 51, 13, 53, 27, 55, 7, 57, 29, 59, 15, 61, 31, 63, 8, 65, 33, 67, 17, 69, 35, 71, 9, 73, 37, 75, 19, 77, 39, 79]

sage: [lcm(n,9)for n in xrange(0, 57)] #A109050  	 	 LCM(n,9).

[0, 9, 18, 9, 36, 45, 18, 63, 72, 9, 90, 99, 36, 117, 126, 45, 144, 153, 18, 171, 180, 63, 198, 207, 72, 225, 234, 27, 252, 261, 90, 279, 288, 99, 306, 315, 36, 333, 342, 117, 360, 369, 126, 387, 396, 45, 414, 423, 144, 441, 450, 153, 468, 477, 54, 495, 504]

sage: [lcm(n,9)/9for n in xrange(0, 78)] #ok A106610  	 	 Numerator of n/(n+9).

[0, 1, 2, 1, 4, 5, 2, 7, 8, 1, 10, 11, 4, 13, 14, 5, 16, 17, 2, 19, 20, 7, 22, 23, 8, 25, 26, 3, 28, 29, 10, 31, 32, 11, 34, 35, 4, 37, 38, 13, 40, 41, 14, 43, 44, 5, 46, 47, 16, 49, 50, 17, 52, 53, 6, 55, 56, 19, 58, 59, 20, 61, 62, 7, 64, 65, 22, 67, 68, 23, 70, 71, 8, 73, 74, 25, 76, 77]

sage: [lcm(n,10)for n in xrange(0, 57)] #ok A109051  	 	 LCM(n,10).

[0, 10, 10, 30, 20, 10, 30, 70, 40, 90, 10, 110, 60, 130, 70, 30, 80, 170, 90, 190, 20, 210, 110, 230, 120, 50, 130, 270, 140, 290, 30, 310, 160, 330, 170, 70, 180, 370, 190, 390, 40, 410, 210, 430, 220, 90, 230, 470, 240, 490, 50, 510, 260, 530, 270, 110, 280]

sage: [lcm(n,10)/10 for n in xrange(0, 79)] #ok A106611  	 	 Numerator of n/(n+10).

[0, 1, 1, 3, 2, 1, 3, 7, 4, 9, 1, 11, 6, 13, 7, 3, 8, 17, 9, 19, 2, 21, 11, 23, 12, 5, 13, 27, 14, 29, 3, 31, 16, 33, 17, 7, 18, 37, 19, 39, 4, 41, 21, 43, 22, 9, 23, 47, 24, 49, 5, 51, 26, 53, 27, 11, 28, 57, 29, 59, 6, 61, 31, 63, 32, 13, 33, 67, 34, 69, 7, 71, 36, 73, 37, 15, 38, 77, 39]

sage: [lcm(n,11)for n in xrange(0, 54)] #ok A109052  	 	 LCM(n,11).

[0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 11, 132, 143, 154, 165, 176, 187, 198, 209, 220, 231, 22, 253, 264, 275, 286, 297, 308, 319, 330, 341, 352, 33, 374, 385, 396, 407, 418, 429, 440, 451, 462, 473, 44, 495, 506, 517, 528, 539, 550, 561, 572, 583]

sage: [lcm(n,11)/11for n in xrange(0, 54)] #ok A106612  	 	 Numerator of n/(n+11).

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 2, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 3, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 4, 45, 46, 47, 48, 49, 50, 51, 52, 53]

sage: [lcm(n,12)for n in xrange(0, 57)] #ok A109053  LCM(n,12).

[0, 12, 12, 12, 12, 60, 12, 84, 24, 36, 60, 132, 12, 156, 84, 60, 48, 204, 36, 228, 60, 84, 132, 276, 24, 300, 156, 108, 84, 348, 60, 372, 96, 132, 204, 420, 36, 444, 228, 156, 120, 492, 84, 516, 132, 180, 276, 564, 48, 588, 300, 204, 156, 636, 108, 660, 168]

sage: [lcm(n,12)/12for n in xrange(0, 72)] #ok A051724  	 	 Numerator of n/12.

[0, 1, 1, 1, 1, 5, 1, 7, 2, 3, 5, 11, 1, 13, 7, 5, 4, 17, 3, 19, 5, 7, 11, 23, 2, 25, 13, 9, 7, 29, 5, 31, 8, 11, 17, 35, 3, 37, 19, 13, 10, 41, 7, 43, 11, 15, 23, 47, 4, 49, 25, 17, 13, 53, 9, 55, 14, 19, 29, 59, 5, 61, 31, 21, 16, 65, 11, 67, 17, 23, 35, 71]

sage: [lcm(n,13)for n in xrange(0, 40)] #nnnnnnnnn

[0, 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 13, 182, 195, 208, 221, 234, 247, 260, 273, 286, 299, 312, 325, 26, 351, 364, 377, 390, 403, 416, 429, 442, 455, 468, 481, 494, 39]

sage: [lcm(n,13)/13for n in xrange(0, 76)] #okA106614  	 	 Numerator of n/(n+13).

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 2, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 3, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 4, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 5, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75]

sage: [lcm(n,14)/14for n in xrange(0, 79)] #ok A106615 Numerator of n/(n+14).

[0, 1, 1, 3, 2, 5, 3, 1, 4, 9, 5, 11, 6, 13, 1, 15, 8, 17, 9, 19, 10, 3, 11, 23, 12, 25, 13, 27, 2, 29, 15, 31, 16, 33, 17, 5, 18, 37, 19, 39, 20, 41, 3, 43, 22, 45, 23, 47, 24, 7, 25, 51, 26, 53, 27, 55, 4, 57, 29, 59, 30, 61, 31, 9, 32, 65, 33, 67, 34, 69, 5, 71, 36, 73, 37, 75, 38, 11, 39]

sage: [lcm(n,15)/15for n in xrange(0, 79)] #ok A106616  	 	 Numerator of n/(n+15).

[0, 1, 2, 1, 4, 1, 2, 7, 8, 3, 2, 11, 4, 13, 14, 1, 16, 17, 6, 19, 4, 7, 22, 23, 8, 5, 26, 9, 28, 29, 2, 31, 32, 11, 34, 7, 12, 37, 38, 13, 8, 41, 14, 43, 44, 3, 46, 47, 16, 49, 10, 17, 52, 53, 18, 11, 56, 19, 58, 59, 4, 61, 62, 21, 64, 13, 22, 67, 68, 23, 14, 71, 24, 73, 74, 5, 76, 77, 26]

sage: [lcm(n,16)for n in xrange(0, 10)] #nnnnnnnnnnnnn

[0, 16, 16, 48, 16, 80, 48, 112, 16, 144]

sage: [lcm(n,16)/16for n in xrange(0, 80)] #ok A106617  	 	 Numerator of n/(n+16).

[0, 1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9, 19, 5, 21, 11, 23, 3, 25, 13, 27, 7, 29, 15, 31, 2, 33, 17, 35, 9, 37, 19, 39, 5, 41, 21, 43, 11, 45, 23, 47, 3, 49, 25, 51, 13, 53, 27, 55, 7, 57, 29, 59, 15, 61, 31, 63, 4, 65, 33, 67, 17, 69, 35, 71, 9, 73, 37, 75, 19, 77, 39, 79]

sage: [lcm(n,17)/17for n in xrange(0, 75)] #ok A106618  	 	 Numerator of n/(n+17).

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 2, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 3, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 4, 69, 70, 71, 72, 73, 74]

sage: [lcm(n,18)/18for n in xrange(0, 80)] #ok A106619  	 	 Numerator of n/(n+18).

[0, 1, 1, 1, 2, 5, 1, 7, 4, 1, 5, 11, 2, 13, 7, 5, 8, 17, 1, 19, 10, 7, 11, 23, 4, 25, 13, 3, 14, 29, 5, 31, 16, 11, 17, 35, 2, 37, 19, 13, 20, 41, 7, 43, 22, 5, 23, 47, 8, 49, 25, 17, 26, 53, 3, 55, 28, 19, 29, 59, 10, 61, 31, 7, 32, 65, 11, 67, 34, 23, 35, 71, 4, 73, 37, 25, 38, 77, 13, 79]

sage: [lcm(n,19)/19for n in xrange(0, 75)] # ok A106620  	 	 Numerator of n/(n+19).

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 2, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 3, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74]

sage: [lcm(20,n)for n in xrange(0, 22)] #nnnnnnnnnnnnnnn

[0, 20, 20, 60, 20, 20, 60, 140, 40, 180, 20, 220, 60, 260, 140, 60, 80, 340, 180, 380, 20, 420]

sage: [lcm(20,n)/10for n in xrange(0, 22)] #nnnnnnnnnn

[0, 2, 2, 6, 2, 2, 6, 14, 4, 18, 2, 22, 6, 26, 14, 6, 8, 34, 18, 38, 2, 42]

sage: [lcm(20,n)/5for n in xrange(0, 22)] #nnnnnnnnnnnn

[0, 4, 4, 12, 4, 4, 12, 28, 8, 36, 4, 44, 12, 52, 28, 12, 16, 68, 36, 76, 4, 84]

sage: [lcm(20,n)/20for n in xrange(0, 80)] #ok A106621  	 	 Numerator of n/(n+20).

[0, 1, 1, 3, 1, 1, 3, 7, 2, 9, 1, 11, 3, 13, 7, 3, 4, 17, 9, 19, 1, 21, 11, 23, 6, 5, 13, 27, 7, 29, 3, 31, 8, 33, 17, 7, 9, 37, 19, 39, 2, 41, 21, 43, 11, 9, 23, 47, 12, 49, 5, 51, 13, 53, 27, 11, 14, 57, 29, 59, 3, 61, 31, 63, 16, 13, 33, 67, 17, 69, 7, 71, 18, 73, 37, 15, 19, 77, 39, 79]

sage: [lcm(21,n)/21for n in xrange(0, 80)] #nnnnnnnnnn

[0, 1, 2, 1, 4, 5, 2, 1, 8, 3, 10, 11, 4, 13, 2, 5, 16, 17, 6, 19, 20, 1, 22, 23, 8, 25, 26, 9, 4, 29, 10, 31, 32, 11, 34, 5, 12, 37, 38, 13, 40, 41, 2, 43, 44, 15, 46, 47, 16, 7, 50, 17, 52, 53, 18, 55, 8, 19, 58, 59, 20, 61, 62, 3, 64, 65, 22, 67, 68, 23, 10, 71, 24, 73, 74, 25, 76, 11, 26, 79]

sage: [lcm(100,n)/100for n in xrange(0, 80)] #nnnnn

[0, 1, 1, 3, 1, 1, 3, 7, 2, 9, 1, 11, 3, 13, 7, 3, 4, 17, 9, 19, 1, 21, 11, 23, 6, 1, 13, 27, 7, 29, 3, 31, 8, 33, 17, 7, 9, 37, 19, 39, 2, 41, 21, 43, 11, 9, 23, 47, 12, 49, 1, 51, 13, 53, 27, 11, 14, 57, 29, 59, 3, 61, 31, 63, 16, 13, 33, 67, 17, 69, 7, 71, 18, 73, 37, 3, 19, 77, 39, 79]

sage: [binomial(n,1)*factorial (n) for n in xrange(0, 22)] #A001563 a(n) = n*n! = (n+1)!-n!.

[0, 1, 4, 18, 96, 600, 4320, 35280, 322560, 3265920, 36288000, 439084800, 5748019200, 80951270400, 1220496076800, 19615115520000, 334764638208000, 6046686277632000, 115242726703104000, 2311256907767808000, 48658040163532800000, 1072909785605898240000]

sage: [binomial(n,2)*factorial (n) for n in xrange(2, 17)] #beküldenii A001804   n!.C(n,2).

[2, 18, 144, 1200, 10800, 105840, 1128960, 13063680, 163296000, 2195424000, 31614105600, 485707622400, 7933224499200, 137305808640000, 2510734786560000]

sage: [binomial(n,2) for n in xrange(2, 21)] #A000217  	 	 Triangular numbers: a(n) = C(n+1,2) = n(n+1)/2 = 0+1+2+...+n. 
0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66,

[1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190]

sage: [factorial (n-1) for n in xrange(2, 21)] #A000142  	 	 Factorial numbers: n! = 1*2*3*4*...*n (order of symmetric group S_n, number of permutations of n letters). 
1, 1, 2, 6, 24, 120, 720, 5040, 40320,

[1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000]

sage: [binomial(n,2)*factorial (n-1) for n in xrange(2, 21)] #beküldenii A001286  	 	 Lah numbers: (n-1)*n!/2.

[1, 6, 36, 240, 1800, 15120, 141120, 1451520, 16329600, 199584000, 2634508800, 37362124800, 566658892800, 9153720576000, 156920924160000, 2845499424768000, 54420176498688000, 1094805903679488000, 23112569077678080000]

sage: [binomial(n,2)*factorial (n-2) for n in xrange(2, 21)] #nem jó	1, 1, 1, 3, 12, 60, 360, 2520..,A001710  	 	 Order of alternating group A_n, or number of even permutations of n letters.

[1, 3, 12, 60, 360, 2520, 20160, 181440, 1814400, 19958400, 239500800, 3113510400, 43589145600, 653837184000, 10461394944000, 177843714048000, 3201186852864000, 60822550204416000, 1216451004088320000]

sage: [binomial(n,3)*factorial (n) for n in xrange(3, 19)] #beküldeni A001805  	 	 n! * C(n,3).

[6, 96, 1200, 14400, 176400, 2257920, 30481920, 435456000, 6586272000, 105380352000, 1780927948800, 31732897996800, 594991837440000, 11716762337280000, 241867451105280000, 5224336943874048000]

sage: [binomial(n,3)*factorial (n)/6 for n in xrange(0, 21)] #ok A001810  	 	 Coefficients of Laguerre polynomials.    	
sage: [factorial(m)*binomial(m, 3)/6 for m in xrange (0, 22)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 05 2008

line 4 [factorial(m)*binomial(m, _sage_const_3 )/_sage_const_6 for m in xrange (_sage_const_0 , _sage_const_22 )] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul _sage_const_05 _sage_const_2008 ^ SyntaxError: invalid syntax

sage: [binomial(n,3)*factorial (n-1) for n in xrange(3, 19)] #nnnnnnnn

[6, 96, 1200, 14400, 176400, 2257920, 30481920, 435456000, 6586272000, 105380352000, 1780927948800, 31732897996800, 594991837440000, 11716762337280000, 241867451105280000, 5224336943874048000]

sage: [binomial(n,3)*factorial (n-1)/2 for n in xrange(1, 21)]#beküldeni A001754  	 Lah numbers: n!*C(n-1,2)/6.

[0, 0, 1, 12, 120, 1200, 12600, 141120, 1693440, 21772800, 299376000, 4390848000, 68497228800, 1133317785600, 19833061248000, 366148823040000, 7113748561920000, 145120470663168000, 3101950060425216000, 69337707233034240000]

sage: [binomial(n,3)*factorial (n-2) for n in xrange(2, 22)] #beküldeni A005990  	 	 (n-1)*(n+1)!/6.

[0, 1, 8, 60, 480, 4200, 40320, 423360, 4838400, 59875200, 798336000, 11416204800, 174356582400, 2833294464000, 48819843072000, 889218570240000, 17072996548608000, 344661117825024000, 7298706024529920000, 161787983543746560000]

sage: [binomial(n,3)*factorial (n-3) for n in xrange(3, 22)] #beküldeni A001715  	 	 n!/6.

[1, 4, 20, 120, 840, 6720, 60480, 604800, 6652800, 79833600, 1037836800, 14529715200, 217945728000, 3487131648000, 59281238016000, 1067062284288000, 20274183401472000, 405483668029440000, 8515157028618240000]

sage: [binomial(n,3)*factorial (n-4) for n in xrange(4, 22)] #nnnnnnnn

[4, 10, 40, 210, 1344, 10080, 86400, 831600, 8870400, 103783680, 1320883200, 18162144000, 268240896000, 4234374144000, 71137485619200, 1267136462592000, 23851980472320000, 473064279367680000]

sage: [binomial(n,3)*factorial (n-4)/2 for n in xrange(4, 22)] #nnnnnnnn

[2, 5, 20, 105, 672, 5040, 43200, 415800, 4435200, 51891840, 660441600, 9081072000, 134120448000, 2117187072000, 35568742809600, 633568231296000, 11925990236160000, 236532139683840000]

sage: [binomial(n,4)*factorial (n) for n in xrange(4, 19)] #bekóldeni
A001806 		n! * C(n,4).

[24, 600, 10800, 176400, 2822400, 45722880, 762048000, 13172544000, 237105792000, 4452319872000, 87265469491200, 1784975512320000, 38079477596160000, 846536078868480000, 19591263539527680000]

sage: [binomial(n,4)*factorial (n)/24 for n in xrange(4, 20)] #ok A001811    Coefficients of Laguerre polynomials.  sage: [factorial(m)*binomial(m, 4)/24 for m in xrange (4, 19)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 05 2008

[1, 25, 450, 7350, 117600, 1905120, 31752000, 548856000, 9879408000, 185513328000, 3636061228800, 74373979680000, 1586644899840000, 35272336619520000, 816302647480320000, 19645683716026368000]

sage: [binomial(n,4)*factorial (n-1)/6 for n in xrange(4, 21)] #okA001755  	 	 Lah numbers: n!C(n-1,3)/4!.

[1, 20, 300, 4200, 58800, 846720, 12700800, 199584000, 3293136000, 57081024000, 1038874636800, 19833061248000, 396661224960000, 8299373322240000, 181400588328960000, 4135933413900288000, 98228418580131840000]

sage: [binomial(n,4)*factorial (n-2)/2 for n in xrange(4, 18)] #okA005461  	 	 Number of simplices in barycentric subdivision of n-simplex.

[1, 15, 180, 2100, 25200, 317520, 4233600, 59875200, 898128000, 14270256000, 239740300800, 4249941696000, 79332244992000, 1556132497920000]

sage: [binomial(n,4)*factorial (n-3) for n in xrange(4, 21)] #ok A061206  	 	 A diagonal of binomial coefficients multiplied by factorials array.

[1, 10, 90, 840, 8400, 90720, 1058400, 13305600, 179625600, 2594592000, 39956716800, 653837184000, 11333177856000, 207484333056000, 4001483566080000, 81096733605888000, 1723305589125120000]

sage: [binomial(n,4)*factorial (n-4) for n in xrange(4, 22)] #ok A001720   n!/24.

[1, 5, 30, 210, 1680, 15120, 151200, 1663200, 19958400, 259459200, 3632428800, 54486432000, 871782912000, 14820309504000, 266765571072000, 5068545850368000, 101370917007360000, 2128789257154560000]

sage: [binomial(n,4)*factorial (n-3)/10 for n in xrange(5, 21)] #nnnnn

[1, 9, 84, 840, 9072, 105840, 1330560, 17962560, 259459200, 3995671680, 65383718400, 1133317785600, 20748433305600, 400148356608000, 8109673360588800, 172330558912512000]

sage: [binomial(n,4)*factorial (n)/720/5 for n in xrange(4, 20)] #nnnnnnnnnnnnnnn

[1/150, 1/6, 3, 49, 784, 63504/5, 211680, 3659040, 65862720, 1236755520, 24240408192, 495826531200, 10577632665600, 235148910796800, 5442017649868800, 130971224773509120]

sage: [binomial(n,5)*factorial (n) for n in xrange(5, 19)] #ok A001807  	 	 n! * C(n,5).

[120, 4320, 105840, 2257920, 45722880, 914457600, 18441561600, 379369267200, 8014175769600, 174530938982400, 3926946127104000, 91390746230784000, 2200993805058048000, 54855537910677504000]

sage: [binomial(n,5)*factorial(n)/factorial(5) for n in xrange(5, 19)] #ok A001812  	 	 Coefficients of Laguerre polynomials. 	 PROGRAM   	

sage: [factorial(m)*binomial(m, 5)/120 for m in xrange (5, 23)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 05 2008

Syntax Error: sage: [factorial(m)*binomial(m, 5)/120 for m in xrange (5, 23)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 05 2008

sage: [binomial(n,5)*factorial (n-1)/factorial (4) for n in xrange(5, 21)] # ok A001777  	 	 Lah numbers: n!C(n-1,4)/5!.

[120, 4320, 105840, 2257920, 45722880, 914457600, 18441561600, 379369267200, 8014175769600, 174530938982400, 3926946127104000, 91390746230784000, 2200993805058048000, 54855537910677504000]

sage: [binomial(n,5)*factorial (n-2)/6 for n in xrange(5, 21)] #ok A062193  	 	 Fourth (unsigned) column sequence of triangle A062139 (generalized a=2 Laguerre).

[1, 24, 420, 6720, 105840, 1693440, 27941760, 479001600, 8562153600, 159826867200, 3116623910400, 63465795993600, 1348648164864000, 29877743960064000, 689322235650048000, 16543733655601152000]

sage: [binomial(n,5)*factorial (n-3)/2 for n in xrange(5, 21)] #ok A062141  	 	 Third column sequence of coefficient triangle A062137 of generalized Laguerre polynomials n!*L(n,3,x).

[1, 18, 252, 3360, 45360, 635040, 9313920, 143700480, 2335132800, 39956716800, 719220902400, 13599813427200, 269729632972800, 5602076992512000, 121645100408832000, 2757288942600192000]

sage: [binomial(n,5)*factorial (n-4) for n in xrange(5, 22)] #ok
A062199 		Second (unsigned) column sequence of triangle A062140 (generalized a=4 Laguerre).

[1, 12, 126, 1344, 15120, 181440, 2328480, 31933440, 467026560, 7264857600, 119870150400, 2092278988800, 38532804710400, 746943599001600, 15205637551104000, 324386934423552000, 7237883474325504000]

sage: [binomial(n,5)*factorial (n-5) for n in xrange(5, 20)] #ok A001725  	 	 n!/5!.

[1, 6, 42, 336, 3024, 30240, 332640, 3991680, 51891840, 726485760, 10897286400, 174356582400, 2964061900800, 53353114214400, 1013709170073600]

sage: [binomial(n,5)*factorial (n-5)/6 for n in xrange(6, 21)] #nemmmm kelll
A001730 		n!/6!.

[1, 7, 56, 504, 5040, 55440, 665280, 8648640, 121080960, 1816214400, 29059430400, 494010316800, 8892185702400, 168951528345600, 3379030566912000]

sage: [binomial(n,5)*factorial (n-6) for n in xrange(6, 20)] #nnnnn

[6, 21, 112, 756, 6048, 55440, 570240, 6486480, 80720640, 1089728640, 15850598400, 247005158400, 4104085708800, 72407797862400]

sage: [binomial(n,5)*factorial (n-7) for n in xrange(7, 20)] #nnnnnnnn

[21, 56, 252, 1512, 11088, 95040, 926640, 10090080, 121080960, 1585059840, 22455014400, 342007142400, 5569830604800]

sage: [binomial(n,6)*factorial (n)/factorial (6)/49 for n in xrange(1, 20)] #nnnnnnnnn

[0, 0, 0, 0, 0, 1/49, 1, 32, 864, 21600, 522720, 12545280, 2120152320/7, 7420533120, 185513328000, 4749141196800, 124772891443200, 3368868068966400, 93550874838220800]

sage: [binomial(n,6)*factorial (n-1)/factorial (5) for n in xrange(6, 22)] #ok A001778  	 	 Lah numbers: n!C(n-1,5)/6!.

[1, 42, 1176, 28224, 635040, 13970880, 307359360, 6849722880, 155831195520, 3636061228800, 87265469491200, 2157837063782400, 55024845126451200, 1447576694865100800, 39291367432052736000, 1100158288097476608000]

sage: [binomial(n,6)*factorial (n-2)/factorial (4) for n in xrange(6, 22)] #ok A062194  	 	 Fifth column sequence of triangle A062139 (generalized a=2 Laguerre).

[1, 35, 840, 17640, 352800, 6985440, 139708800, 2854051200, 59935075200, 1298593296000, 29088489830400, 674324082432000, 16183777978368000, 402104637462528000, 10339833534750720000, 275039572024369152000]

sage: [binomial(n,6)*factorial (n-3)/factorial (3) for n in xrange(6, 22)] #ok A062142  	 	 Fourth (unsigned) column sequence of coefficient triangle A062137 of generalized Laguerre polynomials n!*L(n,3,x).

[1, 28, 560, 10080, 176400, 3104640, 55883520, 1037836800, 19978358400, 399567168000, 8310997094400, 179819755315200, 4045944494592000, 94612855873536000, 2297740785500160000, 57903067794604032000]

sage: [binomial(n,6)*factorial (n-4)/2 for n in xrange(6, 22)] #ok A062260  	 	 Third (unsigned) column sequence of triangle A062140 (generalized a=4 Laguerre).

[1, 21, 336, 5040, 75600, 1164240, 18627840, 311351040, 5448643200, 99891792000, 1917922406400, 38532804710400, 809188898918400, 17739910476288000, 405483668029440000, 9650511299100672000]

sage: [binomial(n,7)*factorial (n)/5040 for n in xrange(1, 20)] #nnnnn

[0, 0, 0, 0, 0, 0, 1, 64, 2592, 86400, 2613600, 75271680, 2120152320, 59364264960, 1669619952000, 47491411968000, 1372501805875200, 40426416827596800, 1216161372896870400]

sage: [stirling_number1(n,1)+factorial (n+2)/6 for n in xrange(1, 16)] #

[2, 5, 22, 126, 864, 6840, 61200, 609840, 6693120, 80196480, 1041465600, 14569632000, 218424729600, 3493358668800, 59368416307200]

sage: [stirling_number1(n,1)*factorial (n+2)/6 for n in xrange(1, 16)] #A010792  	 xxxx	 n! (n+3)! / 3!.

[1, 4, 40, 720, 20160, 806400, 43545600, 3048192000, 268240896000, 28970016768000, 3766102179840000, 579979735695360000, 104396352425164800000, 21714441304434278400000, 5168037030455358259200000]

sage: [stirling_number1(n,1)*factorial (n+1)/2 for n in xrange(1, 16)] #ok van már A010791  	 	n! (n+2)! / 2.

[1, 3, 24, 360, 8640, 302400, 14515200, 914457600, 73156608000, 7242504192000, 869100503040000, 124281371934720000, 20879270485032960000, 4071457744581427200000, 912006534786239692800000]

sage: [stirling_number1(n,1)*factorial (n) for n in xrange(1, 16)] #ok A010790  	 	 n!*(n+1)!.

[1, 2, 12, 144, 2880, 86400, 3628800, 203212800, 14631321600, 1316818944000, 144850083840000, 19120211066880000, 2982752926433280000, 542861032610856960000, 114000816848279961600000]

kkkok A001044  	 	 (n!)^2.  (Other) SAGE:[stirling_number1(n, 1)^2for n in xrange(1, 17)] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 14 2009]

line 3 kkkok A001044 (n!)**_sage_const_2p (Other) SAGE:[stirling_number1(n, _sage_const_1 )**2for n in xrange(_sage_const_1 , _sage_const_17 )] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar _sage_const_14 _sage_const_2009 ] ^ SyntaxError: invalid syntax

sage: [stirling_number1(n,1)*factorial (n-2) for n in xrange(2, 17)] #ok A010790  	 	 n!*(n+1)!.

[1, 2, 12, 144, 2880, 86400, 3628800, 203212800, 14631321600, 1316818944000, 144850083840000, 19120211066880000, 2982752926433280000, 542861032610856960000, 114000816848279961600000]

sage: [stirling_number1(n,1)*factorial(n-3)/2 for n in xrange(3,18)]# ok   A010791  	 	 n! (n+2)! / 2.

[1, 3, 24, 360, 8640, 302400, 14515200, 914457600, 73156608000, 7242504192000, 869100503040000, 124281371934720000, 20879270485032960000, 4071457744581427200000, 912006534786239692800000]

sage: [stirling_number1(n,1)*factorial (n-4)/6 for n in xrange(4, 18)] #ok A010792  	 	 n! (n+3)! / 3!.

[1, 4, 40, 720, 20160, 806400, 43545600, 3048192000, 268240896000, 28970016768000, 3766102179840000, 579979735695360000, 104396352425164800000, 21714441304434278400000]

sage: [stirling_number1(n,1)*factorial (n-5)/factorial (4)for n in xrange(5, 19)] #ok A010793  	 	 n! (n+4)! / 4!.

[1, 5, 60, 1260, 40320, 1814400, 108864000, 8382528000, 804722688000, 94152554496000, 13181357629440000, 2174924008857600000, 417585409700659200000, 92286375543845683200000]

sage: [stirling_number1(n,2)*factorial (n)/2 for n in xrange(1, 16)] #nnnnnnnnnnnnnn

[0, 1, 9, 132, 3000, 98640, 4445280, 263450880, 19882920960, 1862619494400, 212130648576000, 28870346115072000, 4628055365885952000, 863185347076276224000, 185340380630599434240000]

sage: [stirling_number1(n,2)*factorial (n-1)/6 for n in xrange(1, 16)] #nnnnn

[0, 1/6, 1, 11, 200, 5480, 211680, 10977120, 736404480, 62087316480, 6428201472000, 801954058752000, 118668086304768000, 20552032073244672000, 4118675125124431872000]

sage: [stirling_number1(n,2)*factorial (n+1)/6 for n in xrange(1, 16)] #nnnnnnnn

[0, 1, 12, 220, 6000, 230160, 11854080, 790352640, 66276403200, 6829604812800, 848522594304000, 125104833165312000, 21597591707467776000, 4315926735381381120000, 988482030029863649280000]