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

Offset: 1

Author

Christian G. Bower, Oct 15 1999

Keywords

• nonn

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

Crossrefs

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

Formula

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

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