A050340 - OEIS

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A050340

Number of ways of factoring n with 3 levels of parentheses.

1, 1, 1, 5, 1, 5, 1, 15, 5, 5, 1, 25, 1, 5, 5, 55, 1, 25, 1, 25, 5, 5, 1, 105, 5, 5, 15, 25, 1, 35, 1, 170, 5, 5, 5, 145, 1, 5, 5, 105, 1, 35, 1, 25, 25, 5, 1, 425, 5, 25, 5, 25, 1, 105, 5, 105, 5, 5, 1, 205, 1, 5, 25, 571, 5, 35, 1, 25, 5, 35, 1, 660, 1, 5, 25, 25, 5, 35, 1, 425, 55, 5 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,4`
	COMMENTS	`a(n) depends only on prime signature of n (cf. A025487). So a(24) = a(375) since 24=2^33 and 375=35^3 both have prime signature (3,1).`
	FORMULA	`Dirichlet g.f.: prod{n=2 to inf}(1/(1-1/n^s)^A050338(n)).`
	EXAMPLE	`4=(((4)))=(((22)))=(((2)(2)))=(((2))((2)))=(((2)))(((2))).`
	CROSSREFS	`Cf. A001055, A050336-A050341. a(p^k)=A007714. a(A002110)=A000357.` `Sequence in context: A100947 A096940 A141345 * A021955 A055191 A060186` `Adjacent sequences: A050337 A050338 A050339 * A050341 A050342 A050343`
	KEYWORD	`nonn`
	AUTHOR	`Christian G. Bower (bowerc(AT)usa.net), Oct 15 1999.`

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Last modified February 15 21:45 EST 2012. Contains 205860 sequences.