A050332 Number of factorizations of n into distinct numbers with an odd number of prime factors.

1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1

Offset

1,24

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 is in A026424}(1+1/n^s).

a(n) = A050333(A101296(n)). - R. J. Mathar, May 26 2017

Crossrefs

Cf. A026424, A045778, A050333. a(p^k)=A000700. a(A002110)=A003724.

Sequence in context: A341594 A368774 A005087 * A369258 A337930 A340691

Adjacent sequences: A050329 A050330 A050331 * A050333 A050334 A050335

Keyword

nonn

Author

Christian G. Bower, Oct 15 1999

Status

approved