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

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).

Examples

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

Links

• R. J. Mathar, Table of n, a(n) for n = 1..2303

Crossrefs

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

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

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