A308298 Expansion of Sum_{k>=1} mu(k)*log(1 + Sum_{j>=1} x^(prime(j)*k))/k.

0, 1, 1, -1, 0, -1, 1, 0, -1, -1, 2, 1, 0, -3, 0, 1, 3, -2, -1, 0, 4, -3, -1, -5, 6, 2, 2, -11, 4, 4, 13, -16, -5, -8, 30, -8, -7, -33, 42, 8, 16, -82, 27, 19, 95, -116, -21, -45, 223, -82, -40, -264, 326, 46, 135, -629, 242, 99, 752, -942, -105, -421, 1826, -717, -240

Offset: 1

Author

Ilya Gutkovskiy, May 19 2019

Keywords

• sign

Comments

Inverse Euler transform of A010051.

Crossrefs

Cf. A000607, A008683, A010051, A030010.

Programs

Mathematica

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

Formula

-1 + Product_{n>=1} 1/(1 - x^n)^a(n) = g.f. of A010051.