A382513 Expansion of Sum_{p prime} p * x^p / (1 - p * x^p).

0, 2, 3, 4, 5, 17, 7, 16, 27, 57, 11, 145, 13, 177, 368, 256, 17, 1241, 19, 1649, 2530, 2169, 23, 10657, 3125, 8361, 19683, 18785, 29, 107442, 31, 65536, 178478, 131361, 94932, 793585, 37, 524649, 1596520, 1439201, 41, 6997770, 43, 4208945, 16302032

Offset: 1

Author

Ilya Gutkovskiy, Mar 30 2025

Keywords

• nonn

Crossrefs

Cf. A008472, A055225, A069359, A373458, A373459.

Programs

Mathematica

nmax = 45; CoefficientList[Series[Sum[Prime[k] x^Prime[k]/(1 - Prime[k] x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Formula

a(n) = Sum_{p|n, p prime} p^(n/p).