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%I #25 Feb 12 2021 09:18:08
%S 1,5,16,208,688,784,2864,9555,17776,81239
%N Numbers k such that k divides Sum_{j=1..k} j^(k+1-j).
%C Numbers k such that k divides A003101(k).
%C a(11) > 10^5.
%e 1^5 + 2^4 + 3^3 + 4^2 + 5^1 = 65 = 5 * 13. So 5 is a term.
%t Do[If[Mod[Sum[PowerMod[k, n + 1 - k, n], {k, 1, n}], n] == 0, Print[n]], {n, 1, 3000}] (* _Vaclav Kotesovec_, Feb 12 2021 *)
%o (PARI) isok(n) = sum(k=1, n, Mod(k, n)^(n+1-k))==0;
%Y Cf. A003101, A128981, A188775, A341437.
%K nonn,more
%O 1,2
%A _Seiichi Manyama_, Feb 11 2021
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