A329434 Expansion of Sum_{k>=1} (-1 + Product_{j>=1} (1 + x^(k*(2*j - 1)))).

1, 1, 2, 2, 2, 3, 2, 4, 4, 4, 3, 7, 4, 5, 7, 9, 6, 10, 7, 12, 11, 11, 10, 20, 14, 16, 18, 22, 18, 28, 21, 32, 29, 32, 32, 47, 36, 44, 46, 60, 50, 67, 58, 75, 77, 82, 79, 112, 95, 114, 114, 134, 126, 157, 148, 181, 176, 196, 193, 248, 224, 257, 268, 308, 299

Offset

1,3

Comments

Inverse Moebius transform of A000700.

Links

Table of n, a(n) for n=1..65.

Formula

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

G.f.: Sum_{k>=1} A000700(k) * x^k / (1 - x^k).

a(n) = Sum_{d|n} A000700(d).

Mathematica

nmax = 65; CoefficientList[Series[Sum[-1 + Product[(1 + x^(k (2 j - 1))), {j, 1, nmax}], {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Crossrefs

Cf. A000700, A047966, A047968.

Sequence in context: A300066 A286545 A046798 * A157231 A332888 A258596

Adjacent sequences: A329431 A329432 A329433 * A329435 A329436 A329437

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 13 2019

Status

approved