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A325446 The unitary version of Kalmár's function: number of ordered factorizations of n into powers of distinct primes.

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%I A325446 #14 Sep 07 2019 08:13:42
%S A325446 1,1,1,1,1,3,1,1,1,3,1,3,1,3,3,1,1,3,1,3,3,3,1,3,1,3,1,3,1,13,1,1,3,3,
%T A325446 3,3,1,3,3,3,1,13,1,3,3,3,1,3,1,3,3,3,1,3,3,3,3,3,1,13,1,3,3,1,3,13,1,
%U A325446 3,3,13,1,3,1,3,3,3,3,13,1,3,1,3,1,13,3
%N A325446 The unitary version of Kalmár's function: number of ordered factorizations of n into powers of distinct primes.
%H A325446 Amiram Eldar, <a href="/A325446/b325446.txt">Table of n, a(n) for n = 1..10000</a>
%F A325446 a(1) = 1 and a(n) = Sum_{d||n} a(d), where d||n are the unitary divisors of n (d such that gcd(d, n/d) = 1).
%F A325446 a(n) = A000670(A001221(n)).
%F A325446 a(n) = A074206(n) for squarefree n (A005117).
%t A325446 f[0] = 1; f[n_] := f[n] = Sum[Binomial[n, k] * f[n - k], {k, 1, n}]; a[n_] := f[PrimeNu[n]]; Array[a, 100]
%Y A325446 Cf. A001221, A000670, A005117, A074206.
%K A325446 nonn
%O A325446 1,6
%A A325446 _Amiram Eldar_, Sep 06 2019