A050330 - OEIS

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A050330

Number of factorizations of n into numbers with an odd number of prime factors.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 2, 2, 1, 2, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 2, 1, 2, 2, 1, 1, 4, 1, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 4, 1, 1, 2, 4, 1, 2, 1, 2, 1, 2, 1, 5, 1, 1, 2, 2, 1, 2, 1, 4, 2, 1, 1, 4, 1, 1, 1, 3, 1, 4, 1, 2, 1, 1, 1, 6, 1, 2, 2, 3, 1, 2, 1

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OFFSET

1,8

COMMENTS

a(n) depends only on prime signature of n (cf. A025487). So a(24) = a(375) since 24 = 2^3*3 and 375 = 3*5^3 both have prime signature (3,1).

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..2519

FORMULA

Dirichlet g.f.: Product_{n in A026424} (1/(1-1/n^s)).

a(n) = A050331(A101296(n)). - R. J. Mathar, May 26 2017

CROSSREFS

Cf. A001055, A026424, A050331. a(p^k)=A000009. a(A002110)=A003724.