A329435 Expansion of Sum_{k>=1} (-1 + Product_{j>=2} 1 / (1 - x^(k*j))).

0, 1, 1, 3, 2, 6, 4, 10, 9, 15, 14, 29, 24, 39, 44, 65, 66, 102, 105, 154, 170, 225, 253, 356, 385, 503, 583, 749, 847, 1100, 1238, 1572, 1809, 2234, 2579, 3219, 3660, 4484, 5195, 6314, 7245, 8800, 10087, 12141, 14011, 16678, 19196, 22930, 26256, 31099, 35784

Offset: 1

Author

Ilya Gutkovskiy, Nov 13 2019

Keywords

• nonn

Comments

Inverse Moebius transform of A002865.

Crossrefs

Cf. A002865, A047966, A047968, A329436.

Programs

Mathematica

nmax = 51; CoefficientList[Series[Sum[-1 + Product[1/(1 - x^(k j)), {j, 2, nmax}], {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Formula

G.f.: Sum_{k>=1} A002865(k) * x^k / (1 - x^k).

a(n) = Sum_{d|n} A002865(d).