A302234 - OEIS

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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

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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