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
Keywords
Examples
a(48) = 3 because we have [39, 9], [33, 15] and [27, 21].
Links
- Eric Weisstein's World of Mathematics, Composite Number
- Index entries for related partition-counting sequences
Programs
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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]
Formula
G.f.: ((1 + x^2)/(1 + x))*Product_{k>=1} (1 + x^k)/((1 + x^(2*k))*(1 + x^prime(k))).