1,1

A123855[n] = Sum[ Sum[ Prime[i]^j, {i, 1, n}], {j, 1, n}]. Most listed a(n) are the powers of 2, except a(5) = 38, a(8) = 205, a(10) = 316. 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[n] = {2, 3, 5, 7, 13, 17, 19, 31, 47, 59, 61, 71, 101, 103, 107, 109, 137, 149, 151, 157, 167, 181, 197, 211, 223, 227, 229, 269, 317, 337, 349, 353, 379, 383, 389, 401, 421, 439, 449, 457, 463, 479, 521, ...}.

Terms of a(n) that are not powers of 2 are listed in A124238[n] = {38,205,316,736,...}. Corresponding indices n such that a(n) = A124238[k] are n = {5,8,10,12,...}.

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}]

Cf. A123856, A123855 - Sum[ Sum[ Prime[i]^j, {i, 1, n}], {j, 1, n}]. Cf. A086787 - Sum(Sum(i^j, j=1..n), i=1..n).

Cf. A124238.

Sequence in context: A061011 A075090 A088259 this_sequence A048168 A131649 A003199

Adjacent sequences: A123854 A123855 A123856 this_sequence A123858 A123859 A123860

hard,more,nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 13 2006, Oct 15 2006, Oct 22 2006