A050336 Number of ways of factoring n with one level of parentheses.

1, 1, 1, 3, 1, 3, 1, 6, 3, 3, 1, 9, 1, 3, 3, 14, 1, 9, 1, 9, 3, 3, 1, 23, 3, 3, 6, 9, 1, 12, 1, 27, 3, 3, 3, 31, 1, 3, 3, 23, 1, 12, 1, 9, 9, 3, 1, 57, 3, 9, 3, 9, 1, 23, 3, 23, 3, 3, 1, 41, 1, 3, 9, 58, 3, 12, 1, 9, 3, 12, 1, 83, 1, 3, 9, 9, 3, 12, 1, 57, 14, 3, 1, 41, 3, 3, 3, 23, 1, 41, 3, 9

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..2303

Formula

Dirichlet g.f.: Product_{n>=2}(1/(1-1/n^s)^A001055(n)).

a(n) = A050337(A101296(n)). - R. J. Mathar, May 26 2017

Example

12 = (12) = (6*2) = (6)*(2) = (4*3) = (4)*(3) = (3*2*2) = (3*2)*(2) = (3)*(2*2) = (3)*(2)*(2).

Crossrefs

Cf. A001055, A050337, A050338, A050339, A050340, A050341.

a(p^k)=A001970. a(A002110)=A000258.

Sequence in context: A357858 A066637 A317144 * A281113 A361519 A236757

Adjacent sequences: A050333 A050334 A050335 * A050337 A050338 A050339

Keyword

nonn

Author

Christian G. Bower, Oct 15 1999

Status

approved