A329465 Expansion of Sum_{k>=1} (-1 + Product_{j>=1} 1 / (1 - x^(k*j*(j + 1)/2))).

1, 2, 3, 4, 3, 8, 5, 8, 9, 11, 8, 20, 12, 17, 20, 25, 18, 36, 25, 38, 39, 44, 37, 68, 51, 63, 69, 85, 69, 113, 90, 117, 117, 136, 128, 189, 154, 185, 195, 239, 206, 288, 253, 308, 321, 358, 333, 457, 406, 476, 485, 566, 521, 671, 629, 734, 737, 833, 794, 1019

Offset

1,2

Comments

Inverse Moebius transform of A007294.

Links

Table of n, a(n) for n=1..60.

Formula

G.f.: Sum_{k>=1} A007294(k) * x^k / (1 - x^k).

a(n) = Sum_{d|n} A007294(d).

Mathematica

nmax = 60; CoefficientList[Series[Sum[-1 + Product[1/(1 - x^(k j (j + 1)/2)), {j, 1, nmax}], {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Crossrefs

Cf. A007294, A047966, A047968, A329439, A329466.

Sequence in context: A198461 A379739 A228576 * A324195 A339663 A211507

Adjacent sequences: A329462 A329463 A329464 * A329466 A329467 A329468

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 13 2019

Status

approved