A329462 Expansion of Sum_{k>=1} (-1 + Product_{j>=1} (1 + x^(k*j^2))).

1, 1, 1, 2, 2, 1, 1, 2, 2, 3, 1, 2, 2, 2, 2, 3, 2, 2, 1, 5, 2, 1, 1, 2, 4, 4, 2, 3, 3, 5, 1, 3, 1, 3, 3, 4, 2, 2, 3, 6, 3, 4, 1, 2, 5, 3, 1, 3, 3, 8, 3, 6, 3, 4, 3, 4, 2, 4, 2, 7, 3, 4, 4, 4, 7, 4, 1, 5, 3, 7, 2, 4, 2, 6, 7, 3, 3, 9, 3, 8, 5, 5, 2, 7, 6, 4, 5, 3, 4, 14

Offset

1,4

Comments

Inverse Moebius transform of A033461.

Links

Table of n, a(n) for n=1..90.

Formula

G.f.: Sum_{k>=1} A033461(k) * x^k / (1 - x^k).

a(n) = Sum_{d|n} A033461(d).

Mathematica

nmax = 90; CoefficientList[Series[Sum[-1 + Product[(1 + x^(k j^2)), {j, 1, Floor[nmax^(1/2)] + 1}], {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Crossrefs

Cf. A033461, A047966, A047968, A329439.

Sequence in context: A168115 A337530 A269982 * A153864 A345128 A112399

Adjacent sequences: A329459 A329460 A329461 * A329463 A329464 A329465

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 13 2019

Status

approved