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A280912 Number of partitions of n into odd semiprimes (A046315). 1
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, 1, 0, 0, 2, 0, 0, 2, 1, 1, 2, 0, 0, 3, 1, 0, 3, 1, 1, 3, 1, 0, 4, 2, 2, 5, 1, 1, 5, 3, 1, 6, 3, 2, 8, 2, 1, 7, 5, 4, 9, 4, 3, 11, 6, 3, 11, 6, 6, 14, 7, 5, 15, 9, 7, 16, 9, 8, 20, 14, 9, 21, 13, 11, 26, 16, 12, 28, 19, 17, 29, 19, 17, 37, 27 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,31

LINKS

Amiram Eldar, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Semiprime

Index entries for related partition-counting sequences

FORMULA

G.f.: Product_{k>=1} 1/(1 - floor(bigomega(2*k+1)/2)*floor(2/bigomega(2*k+ 1))*x^(2*k+1)), where bigomega(k) is the number of prime divisors of k counted with multiplicity (A001222).

EXAMPLE

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

MATHEMATICA

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

CROSSREFS

Cf. A001222, A001358, A046315, A099773, A101048, A112020.

Sequence in context: A159818 A081827 A100286 * A332662 A029303 A281640

Adjacent sequences:  A280909 A280910 A280911 * A280913 A280914 A280915

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 10 2017

STATUS

approved

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Last modified October 22 15:40 EDT 2021. Contains 348172 sequences. (Running on oeis4.)