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%I #13 May 07 2017 16:31:24
%S 1,0,1,1,1,2,2,3,4,4,6,7,9,11,13,16,19,23,28,33,40,46,55,65,76,89,104,
%T 121,141,163,190,219,253,290,334,383,439,502,573,653,744,845,961,1089,
%U 1234,1395,1576,1780,2007,2259,2544,2856,3209,3598,4033,4516,5051,5644,6304,7033,7843
%N Number of partitions of n into parts with an odd number of prime divisors (counted with multiplicity).
%H Alois P. Heinz, <a href="/A286218/b286218.txt">Table of n, a(n) for n = 0..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeFactor.html">Prime Factor</a>
%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>
%F G.f.: Product_{k>=1} 1/(1 - x^A026424(k)).
%e a(8) = 4 because we have [8], [5, 3], [3, 3, 2] and [2, 2, 2, 2].
%p with(numtheory):
%p a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*add(
%p `if`(bigomega(d)::odd, d, 0), d=divisors(j)), j=1..n)/n)
%p end:
%p seq(a(n), n=0..80); # _Alois P. Heinz_, May 04 2017
%t nmax = 60; CoefficientList[Series[Product[1/(1 - Boole[OddQ[PrimeOmega[k]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A001156, A026424, A285799, A286219.
%K nonn
%O 0,6
%A _Ilya Gutkovskiy_, May 04 2017
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