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

1,4

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).

Links

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

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

Example

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

Crossrefs

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

Sequence in context: A318664 A329031 A264483 * A021955 A055191 A299628

Adjacent sequences: A050337 A050338 A050339 * A050341 A050342 A050343

Keyword

nonn

Author

Christian G. Bower, Oct 15 1999

Status

approved