A382512 Expansion of Sum_{p prime} x^p / (1 - x^p)^p.

0, 1, 1, 2, 1, 6, 1, 4, 6, 10, 1, 16, 1, 14, 30, 8, 1, 30, 1, 45, 56, 22, 1, 48, 70, 26, 45, 98, 1, 196, 1, 16, 132, 34, 420, 96, 1, 38, 182, 350, 1, 588, 1, 308, 615, 46, 1, 160, 924, 740, 306, 481, 1, 198, 2002, 1744, 380, 58, 1, 1605, 1, 62, 3234, 32, 3640

Offset: 1

Author

Ilya Gutkovskiy, Mar 30 2025

Keywords

• nonn

Crossrefs

Cf. A001221, A069359, A157019, A322078, A373458, A373459.

Programs

Mathematica

nmax = 65; CoefficientList[Series[Sum[x^Prime[k]/(1 - x^Prime[k])^Prime[k], {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Formula

a(n) = Sum_{p|n, p prime} binomial(n/p+p-2, p-1).