A050347 Number of ways to factor n into distinct factors with 2 levels of parentheses.

1, 1, 1, 1, 1, 4, 1, 4, 1, 4, 1, 10, 1, 4, 4, 7, 1, 10, 1, 10, 4, 4, 1, 26, 1, 4, 4, 10, 1, 22, 1, 14, 4, 4, 4, 34, 1, 4, 4, 26, 1, 22, 1, 10, 10, 4, 1, 63, 1, 10, 4, 10, 1, 26, 4, 26, 4, 4, 1, 74, 1, 4, 10, 29, 4, 22, 1, 10, 4, 22, 1, 105, 1, 4, 10, 10, 4, 22, 1, 63, 7, 4, 1, 74, 4, 4, 4, 26

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

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

Links

• R. J. Mathar, Table of n, a(n) for n = 1..2159

Crossrefs

Cf. A045778, A050345-A050350. a(p^k)=A050343. a(A002110)=A000307.

Formula

Dirichlet g.f.: Product_{n>=2}(1+1/n^s)^A050345(n).

a(n) = A050348(A101296(n)). - R. J. Mathar, May 26 2017