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%I #10 Aug 03 2019 07:58:15
%S 1,1,1,1,1,1,2,3,4,5,7,9,13,18,25,34,46,61,83,112,153,209,286,387,526,
%T 713,969,1317,1794,2437,3312,4497,6110,8302,11290,15347,20865,28354,
%U 38533,52361,71167,96721,131464,178672,242834,330020,448532,609590,828511,1126037,1530418,2079977,2826896,3841998
%N Number of compositions (ordered partitions) of n into parts with an even number of distinct prime divisors.
%H Amiram Eldar, <a href="/A286225/b286225.txt">Table of n, a(n) for n = 0..7000</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^A030231(k)).
%e a(8) = 4 because we have [6, 1, 1], [1, 6, 1], [1, 1, 6] and [1, 1, 1, 1, 1, 1, 1, 1].
%t nmax = 53; CoefficientList[Series[1/(1 - Sum[Boole[EvenQ[PrimeNu[k]]] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
%Y Cf. A030231, A285798, A286221, A286224.
%K nonn
%O 0,7
%A _Ilya Gutkovskiy_, May 04 2017
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