id:A050336 - OEIS Search Results

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Number of ways of factoring n with one level of parentheses.

+0
5

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; listen)

	OFFSET	`1,4`
	COMMENT	`a(n) depends only on prime signature of n (cf. A025487). So a(24) = a(375) since 24=2^33 and 375=35^3 both have prime signature (3,1).`
	FORMULA	`Dirichlet g.f.: prod{n=2 to inf}(1/(1-1/n^s)^A001055(n)).`
	EXAMPLE	`12=(12)=(62)=(6)(2)=(43)=(4)(3)=(322)=(32)(2)=(3)(22)=(3)(2)(2).`
	CROSSREFS	`Cf. A001055, A050337-A050341. a(p^k)=A001970. a(A002110)=A000258.` `Sequence in context: A146907 A126212 A066637 this_sequence A095250 A135521 A122410` `Adjacent sequences: A050333 A050334 A050335 this_sequence A050337 A050338 A050339`
	KEYWORD	`nonn`
	AUTHOR	`Christian G. Bower (bowerc(AT)usa.net), Oct 15 1999.`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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