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

1,6

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)).

Crossrefs

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

Sequence in context: A174571 A099301 A244971 * A240226 A322515 A330571

Adjacent sequences: A050344 A050345 A050346 * A050348 A050349 A050350

Keyword

nonn

Author

_Christian G. Bower_, Oct 15 1999

Status

approved