%I #28 Apr 09 2017 13:39:31
%S 0,1,3,14,100,115,196,500,189,333,847,1022,1352,1671,1920,3432,3757,
%T 2937,1444,7730,1092,427,4232,8668,15000,13037,19197,20902,1682,17999,
%U 16337,27856,32043,31873,16170,14298,47915,5603,12792,8260,16810,18949,51772,64526
%N a(n) = (Sum_{i=1..n-1} i^(n-2)) mod n^3.
%C 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).
%H Seiichi Manyama, <a href="/A284759/b284759.txt">Table of n, a(n) for n = 1..1000</a>
%H R. Mestrovic, <a href="https://arxiv.org/abs/1211.4570">A congruence modulo n^3 involving two consecutive sums of powers and its applications</a>, arXiv:1211.4570 [math.NT], 2012.
%F a(n) = A076015(n-1) modulo A000578(n).
%p seq(add(i^(n-2),i=1..n-1) mod n^3, n=1..100);
%t Table[Mod[Sum[i^(n - 2), {i, n - 1}], n^3], {n, 44}] (* _Michael De Vlieger_, Apr 02 2017 *)
%o (PARI) a(n) = lift(Mod(sum(i=1, n-1, i^(n-2)), n^3))
%o (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
%Y Cf. A000578, A076015, A088164, A284760.
%K nonn
%O 1,3
%A _Felix Fröhlich_, Apr 02 2017