A050338 Number of ways of factoring n with 2 levels of parentheses.

1, 1, 1, 4, 1, 4, 1, 10, 4, 4, 1, 16, 1, 4, 4, 30, 1, 16, 1, 16, 4, 4, 1, 54, 4, 4, 10, 16, 1, 22, 1, 75, 4, 4, 4, 74, 1, 4, 4, 54, 1, 22, 1, 16, 16, 4, 1, 176, 4, 16, 4, 16, 1, 54, 4, 54, 4, 4, 1, 102, 1, 4, 16, 206, 4, 22, 1, 16, 4, 22, 1, 267, 1, 4, 16, 16, 4, 22, 1, 176, 30, 4, 1, 102

Offset

1,4

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..1679

Formula

Dirichlet g.f.: Product_{n>=2}(1/(1-1/n^s)^A050336(n)).

a(n) = A050339(A101296(n)). - R. J. Mathar, May 26 2017

Example

4 = ((4)) = ((2*2)) = ((2)*(2)) = ((2))*((2)).

Crossrefs

Cf. A001055, A050336-A050341. a(p^k)=A007713. a(A002110)=A000307.

Sequence in context: A097936 A277027 A354969 * A301598 A077088 A348971

Adjacent sequences: A050335 A050336 A050337 * A050339 A050340 A050341

Keyword

nonn

Author

Christian G. Bower, Oct 15 1999

Status

approved