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A339396 Number of partitions of n into an odd number of nonprime parts. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 4 13:53 EDT 2021. Contains 346447 sequences. (Running on oeis4.)