A329466 Expansion of Sum_{k>=1} (-1 + Product_{j>=1} (1 + x^(k*j*(j + 1)/2))).

1, 1, 2, 2, 1, 3, 2, 2, 3, 3, 2, 4, 2, 3, 3, 4, 2, 5, 3, 5, 5, 4, 1, 6, 4, 3, 4, 7, 3, 7, 5, 7, 3, 5, 5, 8, 5, 6, 6, 8, 3, 10, 4, 7, 8, 7, 5, 10, 7, 10, 5, 10, 6, 9, 9, 13, 7, 8, 6, 14, 7, 10, 10, 14, 9, 12, 9, 12, 7, 17, 8, 14, 10, 14, 12, 17, 12, 12, 10, 20

Offset

1,3

Comments

Inverse Moebius transform of A024940.

Links

Table of n, a(n) for n=1..80.

Formula

G.f.: Sum_{k>=1} A024940(k) * x^k / (1 - x^k).

a(n) = Sum_{d|n} A024940(d).

Mathematica

nmax = 80; CoefficientList[Series[Sum[-1 + Product[(1 + x^(k j (j + 1)/2)), {j, 1, nmax}], {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Crossrefs

Cf. A024940, A047966, A047968, A329462, A329465.

Sequence in context: A326394 A228425 A316842 * A347627 A263107 A286528

Adjacent sequences: A329463 A329464 A329465 * A329467 A329468 A329469

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 13 2019

Status

approved