A050374 - OEIS

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A050374

Number of ordered factorizations of n into composite factors.

1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 1, 0, 3, 1, 1, 1, 1, 0, 1, 0, 3, 1, 1, 1, 4, 0, 1, 1, 3, 0, 1, 0, 1, 1, 1, 0, 5, 1, 1, 1, 1, 0, 3, 1, 3, 1, 1, 0, 5, 0, 1, 1, 5, 1, 1, 0, 1, 1, 1, 0, 7, 0, 1, 1, 1, 1, 1, 0, 5, 2, 1, 0, 5, 1, 1, 1, 3, 0, 5, 1, 1, 1, 1, 1, 10, 0, 1, 1, 4, 0, 1 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,16`
	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 given by A005171, all but the first term in A005171 turned 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 composite numbers.`
	CROSSREFS	`Cf. A002033, A002808, A050370-A050375. a(p^k)=A000045(n-1). a(A002110)=A032032.` `Sequence in context: A147768 A167746 A050370 * A047886 A014944 A015879` `Adjacent sequences: A050371 A050372 A050373 * A050375 A050376 A050377`
	KEYWORD	`nonn`
	AUTHOR	`Christian G. Bower (bowerc(AT)usa.net), Nov 15 1999.`

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Last modified February 15 08:49 EST 2012. Contains 205740 sequences.