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%I #9 Aug 03 2019 07:58:09
%S 1,0,1,1,1,3,2,6,7,10,18,22,39,54,81,127,179,282,412,620,940,1384,
%T 2106,3129,4698,7062,10531,15856,23695,35541,53304,79773,119723,
%U 179262,268748,402832,603484,904821,1355652,2031963,3045374,4563604,6840316,10250612,15363248,23024904,34506390
%N Number of compositions (ordered partitions) of n into parts with an odd number of prime divisors (counted with multiplicity).
%H Amiram Eldar, <a href="/A286226/b286226.txt">Table of n, a(n) for n = 0..5000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeFactor.html">Prime Factor</a>
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F G.f.: 1/(1 - Sum_{k>=1} x^A026424(k)).
%e a(5) = 3 because we have [5], [3, 2] and [2, 3].
%t nmax = 46; CoefficientList[Series[1/(1 - Sum[Boole[OddQ[PrimeOmega[k]]] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
%Y Cf. A026424, A286218, A286222, A286224, A286227.
%K nonn
%O 0,6
%A _Ilya Gutkovskiy_, May 04 2017
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