A050347 - OEIS

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

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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..2159

FORMULA

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

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

EXAMPLE

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