A302234 Expansion of Product_{k>=1} (1 - x^k)/(1 - x^prime(k)).

1, -1, 0, 0, -1, 1, -1, 1, -1, 0, 1, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, -1, 1, -1, 1, -2, 1, -1, 0, 1, -1, 1, -2, 2, -1, -1, 2, -1, -1, 2, -2, 2, -1, 1, 0, -1, 1, 0, 1, -2, 2, 0, 0, 2, -1, 0, 0, 1, 0, 0, 1, -2, 0, -1, 0, 0, -2, 2, -3, 0, 2, -2, 1, -1, 1, -2, 1, -1, -1, 1

Offset: 0

Author

Ilya Gutkovskiy, Apr 03 2018

Keywords

• sign

Comments

The difference between the number of partitions of n into an even number of distinct nonprime parts and the number of partitions of n into an odd number of distinct nonprime parts.

Convolution of the sequences A000607 and A010815.

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A000607, A002095, A010815, A018252, A046675, A096258, A302236.

Programs

Mathematica

nmax = 80; CoefficientList[Series[Product[(1 - x^k)/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 80; CoefficientList[Series[Product[(1 - Boole[!PrimeQ[k]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} (1 - x^A018252(k)).