A050328 - OEIS

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A050328

Number of ordered factorizations of n into squarefree numbers > 1.

1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 5, 1, 3, 3, 1, 1, 5, 1, 5, 3, 3, 1, 7, 1, 3, 1, 5, 1, 13, 1, 1, 3, 3, 3, 13, 1, 3, 3, 7, 1, 13, 1, 5, 5, 3, 1, 9, 1, 5, 3, 5, 1, 7, 3, 7, 3, 3, 1, 31, 1, 3, 5, 1, 3, 13, 1, 5, 3, 13, 1, 25, 1, 3, 5, 5, 3, 13, 1, 9, 1, 3, 1, 31, 3, 3, 3, 7, 1, 31, 3, 5, 3, 3, 3, 11, 1, 5 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,6`
	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.: 1/(1-B(s)) where B(s) is d.g.f. of characteristic function of squarefree numbers > 1.` `a(n) = Sum_{d divides n, d<n} A010052(n/d)*a(d). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 25 2002`
	CROSSREFS	`Cf. A002033, A005117, A050329. a(p^k)=1. a(A002110)=A000670.` `Sequence in context: A183096 A029356 A114006 * A191278 A030401 A176187` `Adjacent sequences: A050325 A050326 A050327 * A050329 A050330 A050331`
	KEYWORD	`nonn`
	AUTHOR	`Christian G. Bower (bowerc(AT)usa.net), Oct 15 1999.`

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Last modified February 14 21:47 EST 2012. Contains 205663 sequences.