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A050340 Number of ways of factoring n with 3 levels of parentheses. 5
1, 1, 1, 5, 1, 5, 1, 15, 5, 5, 1, 25, 1, 5, 5, 55, 1, 25, 1, 25, 5, 5, 1, 105, 5, 5, 15, 25, 1, 35, 1, 170, 5, 5, 5, 145, 1, 5, 5, 105, 1, 35, 1, 25, 25, 5, 1, 425, 5, 25, 5, 25, 1, 105, 5, 105, 5, 5, 1, 205, 1, 5, 25, 571, 5, 35, 1, 25, 5, 35, 1, 660, 1, 5, 25, 25, 5, 35, 1, 425, 55, 5 (list; graph; refs; listen; history; text; internal format)
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..1295

FORMULA

Dirichlet g.f.: prod{n=2 to inf}(1/(1-1/n^s)^A050338(n)).

a(n) = A050341(A101296(n)). - R. J. Mathar, May 26 2017

EXAMPLE

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

CROSSREFS

Cf. A001055, A050336-A050341. a(p^k)=A007714. a(A002110)=A000357.

Sequence in context: A318664 A329031 A264483 * A021955 A055191 A299628

Adjacent sequences:  A050337 A050338 A050339 * A050341 A050342 A050343

KEYWORD

nonn

AUTHOR

Christian G. Bower, Oct 15 1999.

STATUS

approved

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Last modified December 10 04:15 EST 2019. Contains 329885 sequences. (Running on oeis4.)