A339395 Number of partitions of n into an even number of nonprime parts.

1, 0, 1, 0, 1, 1, 1, 2, 2, 3, 4, 4, 6, 7, 8, 10, 13, 14, 19, 20, 26, 29, 36, 40, 51, 56, 70, 76, 96, 105, 129, 143, 172, 192, 231, 254, 308, 339, 402, 447, 529, 586, 691, 764, 896, 993, 1159, 1281, 1493, 1652, 1912, 2114, 2445, 2699, 3110, 3436, 3939, 4356, 4982, 5497, 6280

Offset

0,8

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 [8, 1], [6, 1, 1, 1] and [4, 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, A027187, A184198, A302236, A339380, A339396.

Sequence in context: A143038 A029040 A053281 * A228117 A286218 A094997

Adjacent sequences: A339392 A339393 A339394 * A339396 A339397 A339398

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 02 2020

Status

approved