A302236 Expansion of Product_{k>=1} (1 + x^prime(k))/(1 + x^k).

1, -1, 1, -1, 0, 0, -1, 1, -1, 0, 0, 0, 0, 1, -1, 1, 0, 0, 1, 0, 0, 0, -1, 1, 0, -1, 1, -2, 1, 0, 0, 2, -1, 0, 0, -1, 2, -1, -1, 1, -2, 1, 0, 0, 0, -2, -1, 2, 0, 0, 1, -3, 2, -1, 1, 2, -2, -1, -1, 1, 3, 0, -2, 1, -2, 0, 3, 0, 0, -2, -2, 5, 1, 1, -1, -4, 1, -1, 2, 4, -2

Offset

0,28

Comments

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

Convolution of the sequences A000586 and A081362.

Links

Table of n, a(n) for n=0..80.

Index entries for sequences related to partitions

Formula

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

Mathematica

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

Crossrefs

Cf. A000586, A002095, A018252, A048165, A081362, A096258, A302234.

Sequence in context: A330460 A027186 A131962 * A262929 A226862 A226864

Adjacent sequences: A302233 A302234 A302235 * A302237 A302238 A302239

Keyword

sign

Author

Ilya Gutkovskiy, Apr 03 2018

Status

approved