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

1,8

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.

Sequence in context: A354990 A318749 A347708 * A339890 A351408 A205788

Adjacent sequences: A050327 A050328 A050329 * A050331 A050332 A050333

Keyword

nonn

Author

Christian G. Bower, Oct 15 1999

Status

approved