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%I #11 Feb 18 2021 01:34:21
%S 4,8,16,32,38,64,128,205,256,316,512,736,1024,2048,3776,4096,4916,
%T 5888,7736,8192,11138,16384,22287,23308,23924,32768,39538,62336,65536,
%U 71936
%N Composite numbers m that divide A123855(m-1) = Sum_{i=1..m-1} Sum_{j=1..m-1} prime(i)^j.
%C Most listed terms a(n) are the powers of 2, except for n = 5,8,10,12,... Corresponding terms that are not powers of 2 are listed in A124238.
%C It appears that 2^k divides A123855(2^k-1) for all k > 0 (confirmed for 0 < k < 10).
%C Prime p that divide A123855(p-1) are listed in A123856.
%t Do[f=Mod[Sum[Sum[PowerMod[Prime[i],j,n],{i,1,n-1}],{j,1,n-1}],n];If[f==0&&!PrimeQ[n],Print[n]],{n,2,512}]
%Y Cf. A123856, A123855, A086787, A124238.
%K hard,more,nonn
%O 1,1
%A _Alexander Adamchuk_, Oct 13 2006, Oct 15 2006, Oct 22 2006
%E More terms from _Max Alekseyev_, Sep 13 2009
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