%I #19 Feb 27 2021 21:37:10

%S 1,2,3,4,6,7,8,9,11,12,14,16,18,20,21,22,23,24,27,28,31,32,33,36,40,

%T 42,43,44,46,47,48,49,54,56,59,60,62,63,64,66,67,69,71,72,77,79,80,81,

%U 83,84,86,88,92,93,94,96,98,99,100,103

%N Numbers m that divide A123269(m) = Sum_{i=1..m, j=1..m, k=1..m} i^j^k.

%C A123269(m) = Sum_{i=1..m, j=1..m, k=1..m} i^j^k = {1, 28, 7625731729896, ...}.

%C Primes terms are listed in A039787.

%t Do[f=Sum[Mod[Sum[Mod[Sum[PowerMod[i,j^k,n], {i, 1, n}],n], {j, 1, n}],n], {k, 1, n}];If[IntegerQ[f/n],Print[n]],{n,1,103}]

%Y Cf. A123269, A039787, A086787.

%K hard,more,nonn

%O 1,2

%A _Alexander Adamchuk_, Oct 30 2006