A329439 Expansion of Sum_{k>=1} (-1 + Product_{j>=1} 1 / (1 - x^(k*j^2))).

1, 2, 2, 4, 3, 5, 3, 7, 6, 8, 5, 12, 7, 10, 10, 15, 10, 19, 11, 22, 17, 20, 15, 31, 22, 28, 27, 35, 27, 44, 29, 46, 40, 48, 43, 69, 47, 61, 58, 80, 61, 89, 67, 93, 92, 97, 85, 129, 101, 131, 118, 146, 125, 172, 142, 182, 166, 191, 170, 241, 193, 231, 230

Offset: 1

Author

Ilya Gutkovskiy, Nov 13 2019

Keywords

• nonn

Comments

Inverse Moebius transform of A001156.

Crossrefs

Cf. A001156, A047966, A047968.

Programs

Mathematica

nmax = 63; CoefficientList[Series[Sum[-1 + Product[1/(1 - x^(k j^2)), {j, 1, Floor[nmax^(1/2)] + 1}], {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Formula

G.f.: Sum_{k>=1} A001156(k) * x^k / (1 - x^k).

a(n) = Sum_{d|n} A001156(d).