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A101048 Number of partitions of n into semiprimes (a(0) = 1 by convention). 12
1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 2, 0, 2, 1, 3, 2, 3, 1, 5, 3, 5, 4, 7, 4, 9, 7, 10, 8, 13, 10, 17, 13, 18, 17, 25, 21, 29, 25, 34, 34, 43, 37, 51, 49, 61, 59, 73, 69, 89, 87, 103, 103, 124, 122, 148, 149, 172, 176, 206, 208, 244, 248, 281, 293, 337, 344, 391, 405, 456, 479, 537, 553 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

COMMENTS

Semiprime analog of A000607. a(n) <= A002095(n). - Jonathan Vos Post, Oct 01 2007

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: 1/product(product(1-x^(p(i)p(j)), i = 1..j),j = 1..infinity), p(k) is the k-th prime. - Emeric Deutsch, Apr 04 2006

EXAMPLE

a(12) = #{6 + 6, 4 + 4 + 4} = #{2 * (2*3), 3 * (2*2)} = 2.

MAPLE

g:=1/product(product(1-x^(ithprime(i)*ithprime(j)), i=1..j), j=1..30): gser:=series(g, x=0, 75): seq(coeff(gser, x, n), n=1..71); # Emeric Deutsch, Apr 04 2006

MATHEMATICA

terms = 100; CoefficientList[1/Product[1 - x^(Prime[i] Prime[j]), {i, 1, PrimePi[Ceiling[terms/2]]}, {j, 1, i}] + O[x]^terms, x] (* Jean-Fran├žois Alcover, Aug 01 2018 *)

PROG

(Haskell)

a101048 = p a001358_list where

   p _          0 = 1

   p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m

-- Reinhard Zumkeller, Mar 21 2014

CROSSREFS

Cf. A000041, A000607, A101049, A001358, A064911, A002095.

Cf. A112020, A112021.

Cf. A002100.

Sequence in context: A156644 A097808 A114325 * A204389 A070102 A029182

Adjacent sequences:  A101045 A101046 A101047 * A101049 A101050 A101051

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Nov 28 2004

EXTENSIONS

a(0) set to 1 by N. J. A. Sloane, Nov 23 2007

STATUS

approved

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Last modified January 22 13:36 EST 2020. Contains 331149 sequences. (Running on oeis4.)