A050340 Number of ways of factoring n with 3 levels of parentheses.

1, 1, 1, 5, 1, 5, 1, 15, 5, 5, 1, 25, 1, 5, 5, 55, 1, 25, 1, 25, 5, 5, 1, 105, 5, 5, 15, 25, 1, 35, 1, 170, 5, 5, 5, 145, 1, 5, 5, 105, 1, 35, 1, 25, 25, 5, 1, 425, 5, 25, 5, 25, 1, 105, 5, 105, 5, 5, 1, 205, 1, 5, 25, 571, 5, 35, 1, 25, 5, 35, 1, 660, 1, 5, 25, 25, 5, 35, 1, 425, 55, 5

Offset: 1

Author

Christian G. Bower, Oct 15 1999

Keywords

• nonn

Comments

a(n) depends only on the 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

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

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1295

Crossrefs

Cf. A001055, A050336-A050341. a(p^k) = A007714. a(A002110) = A000357.

Formula

Dirichlet g.f.: Product{n=2..infinity} (1/(1-1/n^s)^A050338(n)).

a(n) = A050341(A101296(n)). - R. J. Mathar, May 26 2017