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%I #5 Sep 26 2022 20:17:16
%S 1,0,0,1,0,1,0,0,1,1,0,0,0,1,1,2,0,0,0,0,1,1,0,3,1,1,0,0,0,0,0,0,1,1,
%T 1,4,0,1,1,3,0,0,0,0,0,1,0,0,1,0,1,0,0,3,1,3,1,1,0,5,0,1,0,4,1,0,0,0,
%U 1,0,0,0,0,1,0,0,1,0,0,0,2,1,0,5,1,1,1,3,0,5
%N Number of ordered factorizations of n into numbers > 1 with an even number of prime divisors (prime factors counted with multiplicity).
%F a(1) = 1; a(n) = Sum_{d|n, d < n} A065043(n/d) * a(d).
%t A065043[n_] := Boole[EvenQ[PrimeOmega[n]]]; a[1] = 1; a[n_] := a[n] = Sum[If[d < n, A065043[n/d] a[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 90}]
%Y Cf. A028260, A050334, A065043, A074206, A308063, A353337, A357375.
%K nonn
%O 1,16
%A _Ilya Gutkovskiy_, Sep 25 2022
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