%I
%S 1,0,1,1,2,3,4,8,11,19,28,47,72,116,182,289,460,724,1153,1820,2891,
%T 4572,7249,11482,18190,28821,45651,72338,114582,181549,287597,455647,
%U 721849,1143590,1811753,2870247,4547245,7203933,11412922,18080907,28644799,45380602,71894401,113899027,180444897,285870668
%N Number of compositions (ordered partitions) of n into parts with an odd number of distinct prime divisors.
%H Amiram Eldar, <a href="/A286224/b286224.txt">Table of n, a(n) for n = 0..5000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F G.f.: 1/(1  Sum_{k>=1} x^A030230(k)).
%e a(6) = 4 because we have [4, 2], [3, 3], [2, 4] and [2, 2, 2].
%t nmax = 45; CoefficientList[Series[1/(1  Sum[Boole[OddQ[PrimeNu[k]]] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
%Y Cf. A030230, A285799, A286220, A286225.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, May 04 2017
