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 A050336 Number of ways of factoring n with one level of parentheses. 35
 1, 1, 1, 3, 1, 3, 1, 6, 3, 3, 1, 9, 1, 3, 3, 14, 1, 9, 1, 9, 3, 3, 1, 23, 3, 3, 6, 9, 1, 12, 1, 27, 3, 3, 3, 31, 1, 3, 3, 23, 1, 12, 1, 9, 9, 3, 1, 57, 3, 9, 3, 9, 1, 23, 3, 23, 3, 3, 1, 41, 1, 3, 9, 58, 3, 12, 1, 9, 3, 12, 1, 83, 1, 3, 9, 9, 3, 12, 1, 57, 14, 3, 1, 41, 3, 3, 3, 23, 1, 41, 3, 9 (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..2303 FORMULA Dirichlet g.f.: Product_{n>=2}(1/(1-1/n^s)^A001055(n)). a(n) = A050337(A101296(n)). - R. J. Mathar, May 26 2017 EXAMPLE 12 = (12) = (6*2) = (6)*(2) = (4*3) = (4)*(3) = (3*2*2) = (3*2)*(2) = (3)*(2*2) = (3)*(2)*(2). CROSSREFS Cf. A001055, A050337, A050338, A050339, A050340, A050341. a(p^k)=A001970. a(A002110)=A000258. Sequence in context: A126212 A066637 A317144 * A281113 A236757 A095250 Adjacent sequences:  A050333 A050334 A050335 * A050337 A050338 A050339 KEYWORD nonn AUTHOR Christian G. Bower, Oct 15 1999 STATUS approved

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Last modified January 29 14:07 EST 2020. Contains 331338 sequences. (Running on oeis4.)