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A280287 Number of partitions of n into distinct odd composite numbers (A071904). 1
1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 2, 0, 0, 1, 1, 0, 2, 0, 1, 2, 1, 0, 3, 2, 1, 2, 1, 0, 3, 2, 1, 3, 2, 1, 5, 2, 1, 4, 3, 2, 4, 2, 1, 6, 4, 2, 6, 4, 3, 7, 4, 3, 6, 5, 4, 9, 5, 4, 10, 8, 4, 10, 6, 6, 12, 9, 5, 13, 9, 8, 14, 11, 7, 17, 13, 9, 16, 12, 11, 21 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,37

LINKS

Table of n, a(n) for n=0..105.

Eric Weisstein's World of Mathematics, Composite Number

Index entries for related partition-counting sequences

FORMULA

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

EXAMPLE

a(48) = 3 because we have [39, 9], [33, 15] and [27, 21].

MATHEMATICA

nmax = 105; CoefficientList[Series[(1 + x^2)/(1 + x) Product[(1 + x^k)/((1 + x^(2 k)) (1 + x^Prime[k])), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A002095, A002808, A096258, A023895, A071904, A204389, A280285.

Sequence in context: A276422 A323069 A325334 * A147696 A001842 A216654

Adjacent sequences: A280284 A280285 A280286 * A280288 A280289 A280290

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 31 2016

STATUS

approved

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Last modified November 28 10:02 EST 2022. Contains 358411 sequences. (Running on oeis4.)