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%I #5 Mar 19 2018 22:12:52
%S 1,1,1,1,1,3,1,6,1,1,3,20,1,46,6,3,1,232,1,501,3,10,23,2352,1,34,52,1,
%T 6,24442,3,53243,1,234,330,352,1,550863,804,909,3,2616338,10,5701553,
%U 23,3,4622,27077005,1,8811,34,13864,52,280237217,1,34262,6,54290,68915,2900328380,3,6320545915,169615
%N Number of compositions (ordered partitions) of n into parts having the same number of prime divisors (counted with multiplicity) as n.
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F a(n) = [x^n] 1/(1 - Sum_{bigomega(k) = bigomega(n)} x^k).
%e a(20) = 3 because we have [20], [12, 8] and [8, 12], where 20, 12 and 8 are numbers that are the product of exactly 3 (not necessarily distinct) primes.
%t Table[SeriesCoefficient[1/(1 - Sum[Boole[PrimeOmega[k] == PrimeOmega[n]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 62}]
%Y Cf. A001222, A300982, A300983, A301331, A301332.
%K nonn
%O 0,6
%A _Ilya Gutkovskiy_, Mar 18 2018
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