id:A050354 - OEIS Search Results

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Number of ordered factorizations of n with one level of parentheses.

+0
3

1, 1, 1, 3, 1, 5, 1, 9, 3, 5, 1, 21, 1, 5, 5, 27, 1, 21, 1, 21, 5, 5, 1, 81, 3, 5, 9, 21, 1, 37, 1, 81, 5, 5, 5, 111, 1, 5, 5, 81, 1, 37, 1, 21, 21, 5, 1, 297, 3, 21, 5, 21, 1, 81, 5, 81, 5, 5, 1, 201, 1, 5, 21, 243, 5, 37, 1, 21, 5, 37, 1, 513, 1, 5, 21, 21, 5, 37, 1, 297, 27, 5, 1, 201 (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.: (2-zeta(s))/(3-2zeta(s)).` `Recurrence for number of ordered factorizations of n with k-1 levels of parentheses is a(n) = kSum_{d\|n, d<n} a(d), n>1, a(1)= 1/k. - Vladeta Jovovic (vladeta(AT)Eunet.yu), May 25 2005`
	EXAMPLE	`6=(6)=(32)=(23)=(3)(2)=(2)(3).`
	CROSSREFS	`Cf. A002033, A050351-A050359. a(p^k)=3^(k-1). a(A002110)=A050351.` `Adjacent sequences: A050351 A050352 A050353 this_sequence A050355 A050356 A050357` `Sequence in context: A029669 A050329 A051707 this_sequence A126213 A133730 A112031`
	KEYWORD	`nonn`
	AUTHOR	`Christian G. Bower (bowerc(AT)usa.net), Oct 15 1999.`

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Last modified October 15 09:18 EDT 2008. Contains 145015 sequences.

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