A050358 - OEIS

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A050358

Number of ordered factorizations of n with 3 levels of parentheses.

1, 1, 1, 5, 1, 9, 1, 25, 5, 9, 1, 65, 1, 9, 9, 125, 1, 65, 1, 65, 9, 9, 1, 425, 5, 9, 25, 65, 1, 121, 1, 625, 9, 9, 9, 605, 1, 9, 9, 425, 1, 121, 1, 65, 65, 9, 1, 2625, 5, 65, 9, 65, 1, 425, 9, 425, 9, 9, 1, 1145, 1, 9, 65, 3125, 9, 121, 1, 65, 9, 121, 1, 4825, 1, 9, 65, 65, 9, 121 (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 given by A050356, turning all but the first element of A050356 negative. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 15 2010]`
	FORMULA	`Dirichlet g.f.: (4-3zeta(s))/(5-4zeta(s)).`
	EXAMPLE	`6=(((6)))=(((32)))=(((23)))=(((3)(2)))=(((2)(3)))=(((3))((2)))=(((2))((3)))=(((3)))(((2)))=(((2)))(((3))).`
	CROSSREFS	`Cf. A002033, A050351-A050359. a(p^k)=5^(k-1). a(A002110)=A050353.` `Sequence in context: A147423 A147085 A046580 * A147319 A147326 A143114` `Adjacent sequences: A050355 A050356 A050357 * A050359 A050360 A050361`
	KEYWORD	`nonn`
	AUTHOR	`Christian G. Bower (bowerc(AT)usa.net), Oct 15 1999.`

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Last modified February 14 23:53 EST 2012. Contains 205689 sequences.