id:A050358 - OEIS Search Results

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

+0
1

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; 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.: (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 this_sequence A147319 A147326 A143114` `Adjacent sequences: A050355 A050356 A050357 this_sequence A050359 A050360 A050361`
	KEYWORD	`nonn`
	AUTHOR	`Christian G. Bower (bowerc(AT)usa.net), Oct 15 1999.`

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Last modified December 6 13:45 EST 2009. Contains 170429 sequences.

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