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

0,26

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

Table of n, a(n) for n=0..79.

Index entries for sequences related to partitions

Formula

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

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]

Crossrefs

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

Sequence in context: A326017 A290307 A206588 * A345007 A026920 A060763

Adjacent sequences: A302231 A302232 A302233 * A302235 A302236 A302237

Keyword

sign

Author

Ilya Gutkovskiy, Apr 03 2018

Status

approved