A050363 - OEIS

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A050363

Number of ordered factorizations into prime powers greater than 1.

1, 1, 1, 2, 1, 2, 1, 4, 2, 2, 1, 5, 1, 2, 2, 8, 1, 5, 1, 5, 2, 2, 1, 12, 2, 2, 4, 5, 1, 6, 1, 16, 2, 2, 2, 14, 1, 2, 2, 12, 1, 6, 1, 5, 5, 2, 1, 28, 2, 5, 2, 5, 1, 12, 2, 12, 2, 2, 1, 18, 1, 2, 5, 32, 2, 6, 1, 5, 2, 6, 1, 37, 1, 2, 5, 5, 2, 6, 1, 28, 8, 2, 1, 18, 2, 2, 2, 12, 1, 18, 2, 5, 2, 2, 2, 64 (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).` `The Dirichlet inverse is in A010055, turning all but the first element in A010055 negative. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 15 2010]`
	FORMULA	`Dirichlet g.f.: 1/(1-B(s)) where B(s) is d.g.f. of characteristic function of prime powers >1.`
	CROSSREFS	`Cf. A000961, A050360-A050364. a(p^k)=2^(n-1). a(A002110)=A000142=n!.` `Sequence in context: A072342 A066389 A077191 * A166974 A111588 A070972` `Adjacent sequences: A050360 A050361 A050362 * A050364 A050365 A050366`
	KEYWORD	`nonn`
	AUTHOR	`Christian G. Bower (bowerc(AT)usa.net), Oct 15 1999.`

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Last modified February 14 22:12 EST 2012. Contains 205670 sequences.