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A050345 Number of ways to factor n into distinct factors with one level of parentheses. 6
1, 1, 1, 1, 1, 3, 1, 3, 1, 3, 1, 6, 1, 3, 3, 4, 1, 6, 1, 6, 3, 3, 1, 13, 1, 3, 3, 6, 1, 12, 1, 7, 3, 3, 3, 15, 1, 3, 3, 13, 1, 12, 1, 6, 6, 3, 1, 25, 1, 6, 3, 6, 1, 13, 3, 13, 3, 3, 1, 31, 1, 3, 6, 12, 3, 12, 1, 6, 3, 12, 1, 37, 1, 3, 6, 6, 3, 12, 1, 25, 4, 3, 1, 31, 3, 3, 3, 13, 1, 31, 3, 6, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Each "part" in parentheses is distinct from all others at the same level. Thus (3*2)*(2) is allowed but (3)*(2*2) and (3*2*2) are not.

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..2519

FORMULA

Dirichlet g.f.: Product_{n>=2}(1+1/n^s)^A045778(n).

a(n) = A050346(A025487^(-1)(A046523(n))), where A025487^(-1) is the inverse with A025487^(-1)(A025487(n))=n. - R. J. Mathar, May 25 2017

a(n) = A050346(A101296(n)). - Antti Karttunen, May 25 2017

EXAMPLE

12 = (12) = (6*2) = (6)*(2) = (4*3) = (4)*(3) = (3*2)*(2).

CROSSREFS

Cf. A045778, A050346-A050350. a(p^k)=A050342. a(A002110)=A000258.

Sequence in context: A294788 A254578 A296120 * A070039 A227991 A319137

Adjacent sequences:  A050342 A050343 A050344 * A050346 A050347 A050348

KEYWORD

nonn

AUTHOR

Christian G. Bower, Oct 15 1999

STATUS

approved

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Last modified December 12 01:57 EST 2019. Contains 329948 sequences. (Running on oeis4.)