id:A050363 - OEIS Search Results

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Number of ordered factorizations into prime powers greater than 1.

+0
2

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; listen)

	OFFSET	`1,4`
	COMMENT	`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 prime powers >1.`
	CROSSREFS	`Cf. A000961, A050360-A050364. a(p^k)=2^(n-1). a(A002110)=A000142=n!.` `Sequence in context: A072342 A066389 A077191 this_sequence A166974 A111588 A070972` `Adjacent sequences: A050360 A050361 A050362 this_sequence A050364 A050365 A050366`
	KEYWORD	`nonn`
	AUTHOR	`Christian G. Bower (bowerc(AT)usa.net), Oct 15 1999.`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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