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A280285 Number of partitions of n into odd composite numbers (A071904). 2
1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 2, 0, 0, 2, 0, 0, 2, 1, 1, 3, 0, 0, 3, 1, 0, 4, 1, 1, 5, 1, 0, 5, 2, 2, 6, 2, 1, 8, 3, 1, 8, 3, 2, 11, 3, 2, 12, 5, 4, 13, 5, 3, 16, 8, 4, 18, 7, 6, 22, 9, 7, 24, 12, 9, 28, 12, 9, 33, 18, 11, 36, 18, 14, 45, 22, 16, 48, 26, 22, 54, 29, 23, 66, 38 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,28

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Composite Number

Index entries for related partition-counting sequences

FORMULA

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

EXAMPLE

a(36) = 3 because we have [27, 9], [21, 15] and [9, 9, 9, 9].

MAPLE

a:= proc(n) option remember; `if`(n=0, 1, add(add(

`if`(d>1 and d::odd and not isprime(d), d, 0),

d=numtheory[divisors](j))*a(n-j), j=1..n)/n)

end:

seq(a(n), n=0..100); # Alois P. Heinz, Dec 31 2016

MATHEMATICA

nmax = 100; CoefficientList[Series[(1 - x)/(1 - x^2) Product[(1 - x^(2 k)) (1 - x^Prime[k])/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A002095, A002808, A023895, A071904, A204389, A280287.

Sequence in context: A096142 A216921 A344982 * A033719 A171608 A307985

Adjacent sequences: A280282 A280283 A280284 * A280286 A280287 A280288

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 31 2016

STATUS

approved

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Last modified December 7 08:24 EST 2022. Contains 358649 sequences. (Running on oeis4.)