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A123857
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Composite numbers n that divide A123855(n-1) = Sum[ Sum[ Prime[i]^j, {i,1,n-1}], {j,1,n-1}].
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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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.
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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}]
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CROSSREFS
| Cf. A123856, A123855, A086787, A124238.
Sequence in context: A181800 A075090 A088259 * A048168 A175341 A131649
Adjacent sequences: A123854 A123855 A123856 * A123858 A123859 A123860
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KEYWORD
| hard,more,nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 13 2006, Oct 15 2006, Oct 22 2006
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EXTENSIONS
| More terms from Max Alekseyev (maxale(AT)gmail.com), Sep 13 2009
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