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

Author

Alexander Adamchuk, Oct 13 2006, Oct 15 2006, Oct 22 2006

Keywords

• hard
• more
• nonn

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.

Crossrefs

Cf. A123856, A123855, A086787, A124238.

Programs

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}]

Extensions

More terms from Max Alekseyev, Sep 13 2009