A280287 Number of partitions of n into distinct odd composite numbers (A071904).

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

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: A323069 A378875 A325334 * A147696 A001842 A216654

Adjacent sequences: A280284 A280285 A280286 * A280288 A280289 A280290

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 31 2016

Status

approved