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%I #5 Mar 19 2018 22:12:46
%S 1,1,1,1,2,3,1,8,11,19,1,47,2,116,1,1,460,724,4,1820,4,3,6,11482,10,
%T 28821,11,72338,16,181549,1,455647,721847,18,44,14,67,7203907,82,49,
%U 119,45380392,1,113898439,223,141,326,717490903,472,1800800888,614,407,884,11343951113,1268,790,1692,1185
%N Number of compositions (ordered partitions) of n into parts having the same number of distinct prime divisors as n.
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F a(n) = [x^n] 1/(1 - Sum_{omega(k) = omega(n)} x^k).
%e a(18) = 4 because we have [18], [12, 6], [6, 12] and [6, 6, 6], where 18, 12 and 6 are numbers that are divisible by exactly 2 different primes.
%t Table[SeriesCoefficient[1/(1 - Sum[Boole[PrimeNu[k] == PrimeNu[n]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 57}]
%Y Cf. A001221, A300979, A300980, A301331, A301333.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, Mar 18 2018