A123857 Composite numbers m that divide A123855(m-1) = Sum_{i=1..m-1} Sum_{j=1..m-1} prime(i)^j.

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.

Links

Table of n, a(n) for n=1..30.

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

Cf. A123856, A123855, A086787, A124238.

Sequence in context: A322793 A283052 A088259 * A217313 A101434 A293780

Adjacent sequences: A123854 A123855 A123856 * A123858 A123859 A123860

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