A339396 Number of partitions of n into an odd number of nonprime parts.

0, 1, 0, 1, 1, 1, 2, 1, 3, 3, 4, 4, 6, 6, 9, 9, 13, 14, 18, 20, 26, 29, 37, 39, 51, 57, 69, 78, 95, 105, 129, 141, 173, 192, 231, 255, 306, 340, 403, 446, 531, 585, 691, 764, 896, 995, 1160, 1279, 1493, 1652, 1911, 2117, 2443, 2700, 3109, 3434, 3941, 4357, 4983, 5496, 6277

Offset

0,7

Links

Table of n, a(n) for n=0..60.

Index entries for sequences related to partitions

Formula

G.f.: (1/2) * (Product_{k>=1} (1 - x^prime(k)) / (1 - x^k) - Product_{k>=1} (1 + x^prime(k)) / (1 + x^k)).

a(n) = (A002095(n) - A302236(n)) / 2.

Example

a(9) = 3 because we have [9], [4, 4, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1].

Mathematica

nmax = 60; CoefficientList[Series[(1/2) (Product[(1 - x^Prime[k])/(1 - x^k), {k, 1, nmax}] - Product[(1 + x^Prime[k])/(1 + x^k), {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A002095, A018252, A027193, A184199, A302236, A339381, A339395.

Sequence in context: A187498 A029137 A323054 * A027157 A112194 A238788

Adjacent sequences: A339393 A339394 A339395 * A339397 A339398 A339399

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 02 2020

Status

approved