A050338 - OEIS

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A050338

Number of ways of factoring n with 2 levels of parentheses.

1, 1, 1, 4, 1, 4, 1, 10, 4, 4, 1, 16, 1, 4, 4, 30, 1, 16, 1, 16, 4, 4, 1, 54, 4, 4, 10, 16, 1, 22, 1, 75, 4, 4, 4, 74, 1, 4, 4, 54, 1, 22, 1, 16, 16, 4, 1, 176, 4, 16, 4, 16, 1, 54, 4, 54, 4, 4, 1, 102, 1, 4, 16, 206, 4, 22, 1, 16, 4, 22, 1, 267, 1, 4, 16, 16, 4, 22, 1, 176, 30, 4, 1, 102

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OFFSET

1,4

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..1679

FORMULA

Dirichlet g.f.: Product_{n>=2}(1/(1-1/n^s)^A050336(n)).

a(n) = A050339(A101296(n)). - R. J. Mathar, May 26 2017

EXAMPLE

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