

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).
(Formerly M0205 N0076)


5



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
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OFFSET

1,20


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), 217221. 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


EXAMPLE

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


PROG

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


CROSSREFS

Cf. A006881, A073576, A101048.
Sequence in context: A112792 A138319 A217864 * A108352 A215883 A277024
Adjacent sequences: A002097 A002098 A002099 * A002101 A002102 A002103


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Benoit Cloitre, Jun 01 2003


STATUS

approved



