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A050356 Number of ordered factorizations of n with 2 levels of parentheses. 3
1, 1, 1, 4, 1, 7, 1, 16, 4, 7, 1, 40, 1, 7, 7, 64, 1, 40, 1, 40, 7, 7, 1, 208, 4, 7, 16, 40, 1, 73, 1, 256, 7, 7, 7, 292, 1, 7, 7, 208, 1, 73, 1, 40, 40, 7, 1, 1024, 4, 40, 7, 40, 1, 208, 7, 208, 7, 7, 1, 544, 1, 7, 40, 1024, 7, 73, 1, 40, 7, 73, 1, 1840, 1, 7, 40, 40, 7, 73, 1 (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=2^3*3 and 375=3*5^3 both have prime signature (3,1).

FORMULA

Dirichlet g.f.: (3-2*zeta(s))/(4-3*zeta(s)).

EXAMPLE

6=((6))=((3*2))=((2*3))=((3)*(2))=((2)*(3))=((3))*((2))=((2))*((3)).

CROSSREFS

Cf. A002033, A050351-A050359. a(p^k)=4^(k-1). a(A002110)=A050352.

Sequence in context: A157259 A046551 A065814 * A158860 A037022 A037023

Adjacent sequences:  A050353 A050354 A050355 * A050357 A050358 A050359

KEYWORD

nonn

AUTHOR

Christian G. Bower (bowerc(AT)usa.net), Oct 15 1999.

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Last modified February 15 10:06 EST 2012. Contains 205763 sequences.