A284759 a(n) = (Sum_{i=1..n-1} i^(n-2)) mod n^3.

0, 1, 3, 14, 100, 115, 196, 500, 189, 333, 847, 1022, 1352, 1671, 1920, 3432, 3757, 2937, 1444, 7730, 1092, 427, 4232, 8668, 15000, 13037, 19197, 20902, 1682, 17999, 16337, 27856, 32043, 31873, 16170, 14298, 47915, 5603, 12792, 8260, 16810, 18949, 51772, 64526

Offset

1,3

Comments

Conjecture: For n > 1, a(n) = 0 if and only if n is a term of A088164, i.e., n is a Wolstenholme prime (cf. Mestrovic, 2012, Conjecture 2.10).

Links

Seiichi Manyama, Table of n, a(n) for n = 1..1000

R. Mestrovic, A congruence modulo n^3 involving two consecutive sums of powers and its applications, arXiv:1211.4570 [math.NT], 2012.

Formula

a(n) = A076015(n-1) modulo A000578(n).

Maple

seq(add(i^(n-2), i=1..n-1) mod n^3, n=1..100);

Mathematica

Table[Mod[Sum[i^(n - 2), {i, n - 1}], n^3], {n, 44}] (* Michael De Vlieger, Apr 02 2017 *)

Prog

(PARI) a(n) = lift(Mod(sum(i=1, n-1, i^(n-2)), n^3))
(PARI) a(n)=my(m=n^3, e=n-2); lift(sum(i=1, n-1, Mod(i, m)^e)) \\ Charles R Greathouse IV, Apr 07 2017

Crossrefs

Cf. A000578, A076015, A088164, A284760.

Sequence in context: A038051 A132008 A140963 * A284760 A076015 A004659

Adjacent sequences: A284756 A284757 A284758 * A284760 A284761 A284762

Keyword

nonn

Author

Felix Fröhlich, Apr 02 2017

Status

approved