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A050349 Number of ways to factor n into distinct factors with 3 levels of parentheses. 2
1, 1, 1, 1, 1, 5, 1, 5, 1, 5, 1, 15, 1, 5, 5, 11, 1, 15, 1, 15, 5, 5, 1, 45, 1, 5, 5, 15, 1, 35, 1, 25, 5, 5, 5, 65, 1, 5, 5, 45, 1, 35, 1, 15, 15, 5, 1, 130, 1, 15, 5, 15, 1, 45, 5, 45, 5, 5, 1, 145, 1, 5, 15, 60, 5, 35, 1, 15, 5, 35, 1, 240, 1, 5, 15, 15, 5, 35, 1, 130, 11, 5, 1, 145, 5 (list; graph; refs; listen; history; text; internal format)
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..1727

FORMULA

Dirichlet g.f.: Product_{n>=2}(1+1/n^s)^A050347(n).

a(n) = A050350(A101296(n)). - R. J. Mathar, May 26 2017

EXAMPLE

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

CROSSREFS

Cf. A045778, A050345-A050350. a(p^k)=A050344. a(A002110)=A000357.

Sequence in context: A021070 A176260 A098190 * A083528 A056957 A224834

Adjacent sequences:  A050346 A050347 A050348 * A050350 A050351 A050352

KEYWORD

nonn

AUTHOR

Christian G. Bower, Oct 15 1999

STATUS

approved

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Last modified February 19 20:51 EST 2019. Contains 320328 sequences. (Running on oeis4.)