A050338 - OEIS

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A050338

Number of ways of factoring n with 2 levels of parentheses.

1, 1, 1, 4, 1, 4, 1, 10, 4, 4, 1, 16, 1, 4, 4, 30, 1, 16, 1, 16, 4, 4, 1, 54, 4, 4, 10, 16, 1, 22, 1, 75, 4, 4, 4, 74, 1, 4, 4, 54, 1, 22, 1, 16, 16, 4, 1, 176, 4, 16, 4, 16, 1, 54, 4, 54, 4, 4, 1, 102, 1, 4, 16, 206, 4, 22, 1, 16, 4, 22, 1, 267, 1, 4, 16, 16, 4, 22, 1, 176, 30, 4, 1, 102 (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)^A050336(n)).`
	EXAMPLE	`4=((4))=((22))=((2)(2))=((2))*((2)).`
	CROSSREFS	`Cf. A001055, A050336-A050341. a(p^k)=A007713. a(A002110)=A000307.` `Sequence in context: A193454 A089655 A097936 * A077088 A156896 A002193` `Adjacent sequences: A050335 A050336 A050337 * A050339 A050340 A050341`
	KEYWORD	`nonn`
	AUTHOR	`Christian G. Bower (bowerc(AT)usa.net), Oct 15 1999.`

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Last modified February 16 09:00 EST 2012. Contains 205904 sequences.