A050349 Number of ways to factor n into distinct factors with 3 levels of parentheses.

1, 1, 1, 1, 1, 5, 1, 5, 1, 5, 1, 15, 1, 5, 5, 11, 1, 15, 1, 15, 5, 5, 1, 45, 1, 5, 5, 15, 1, 35, 1, 25, 5, 5, 5, 65, 1, 5, 5, 45, 1, 35, 1, 15, 15, 5, 1, 130, 1, 15, 5, 15, 1, 45, 5, 45, 5, 5, 1, 145, 1, 5, 15, 60, 5, 35, 1, 15, 5, 35, 1, 240, 1, 5, 15, 15, 5, 35, 1, 130, 11, 5, 1, 145, 5

Offset

1,6

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..1727

Formula

Dirichlet g.f.: Product_{n>=2}(1+1/n^s)^A050347(n).

a(n) = A050350(A101296(n)). - R. J. Mathar, May 26 2017

Example

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

Crossrefs

Cf. A045778, A050345-A050350. a(p^k)=A050344. a(A002110)=A000357.

Sequence in context: A176260 A098190 A339353 * A083528 A056957 A224834

Adjacent sequences: A050346 A050347 A050348 * A050350 A050351 A050352

Keyword

nonn

Author

Christian G. Bower, Oct 15 1999

Status

approved