A002100 a(n) = number of partitions of n into semiprimes (more precisely, number of ways of writing n as a sum of products of 2 distinct primes).

0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0, 2, 1, 3, 2, 3, 1, 4, 2, 4, 3, 5, 4, 7, 3, 6, 5, 8, 6, 10, 6, 10, 9, 12, 9, 15, 11, 16, 14, 18, 14, 22, 19, 25, 22, 27, 23, 33, 29, 36, 33, 40, 38, 49, 43, 53, 51, 61, 57, 71, 64, 77, 76, 89, 86, 102, 96, 113, 111, 128, 125

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			a(20) = 2: 20 = 2*3 + 2*7 = 2*5 + 2*5.
		

References

• L. M. Chawla and S. A. Shad, On a restricted partition function t(n) and its table, J. Natural Sciences and Mathematics, 9 (1969), 217-221. Math. Rev. 41 #6761.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A006881, A073576, A101048.

Programs

Haskell

a002100 = p a006881_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

Mathematica

a[n_] := SeriesCoefficient[1/Product[If[SquareFreeQ[k] && PrimeNu[k] == 2, 1 - z^k, 1], {k, 1, n}], {z, 0, n}];
Array[a, 100] (* Jean-François Alcover, Nov 26 2020, after PARI *)

PARI

a(n)=polcoeff(1/prod(k=1,n,if(issquarefree(k)*if(omega(k)-2,0,1),1-z^k,1))+O(z^(n+1)),n)

Extensions

More terms from Benoit Cloitre, Jun 01 2003