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A123857
Composite numbers m that divide A123855(m-1) = Sum_{i=1..m-1} Sum_{j=1..m-1} prime(i)^j.
3
4, 8, 16, 32, 38, 64, 128, 205, 256, 316, 512, 736, 1024, 2048, 3776, 4096, 4916, 5888, 7736, 8192, 11138, 16384, 22287, 23308, 23924, 32768, 39538, 62336, 65536, 71936
OFFSET
1,1
COMMENTS
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.
It appears that 2^k divides A123855(2^k-1) for all k > 0 (confirmed for 0 < k < 10).
Prime p that divide A123855(p-1) are listed in A123856.
MATHEMATICA
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}]
CROSSREFS
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Oct 13 2006, Oct 15 2006, Oct 22 2006
EXTENSIONS
More terms from Max Alekseyev, Sep 13 2009
STATUS
approved