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Search: id:A163590
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| 1, 1, 1, 3, 3, 15, 5, 35, 35, 315, 63, 693, 231, 3003, 429, 6435, 6435, 109395, 12155, 230945, 46189, 969969, 88179, 2028117, 676039, 16900975, 1300075, 35102025, 5014575, 145422675, 9694845, 300540195
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Let n$ denote the swinging factorial. a(n) = n$ / 2^sigma(n) where sigma(n) is the exponent of 2 in the prime-factorisation of n$. sigma(n) can be computed as the number of '1's in the base 2 representation of floor(n/2).
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REFERENCES
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Peter Luschny, "Divide, swing and conquer the factorial and the lcm{1,2,...,n}", preprint, April 2008.
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LINKS
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Peter Luschny, Swinging Factorial.
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EXAMPLE
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11$ = 2772 = 2^2*3^2*7*11. Therefore a(11) = 3^2*7*11 = 2772/4 = 693.
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MAPLE
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swing := proc(n) option remember; if n = 0 then 1 elif irem(n, 2) = 1 then swing(n-1)*n else 4*swing(n-1)/n fi end:
sigma := n -> 2^(add(i, i= convert(iquo(n, 2), base, 2))):
a := n -> swing(n)/sigma(n);
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CROSSREFS
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Cf. A056040 and A151565. A001790 = a(2*n), A001803(n) = a(2*n+1).
Sequence in context: A100371 A100347 A165405 this_sequence A114320 A086116 A100735
Adjacent sequences: A163587 A163588 A163589 this_sequence A163591 A163592 A163593
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KEYWORD
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nonn
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AUTHOR
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Peter Luschny (peter(AT)luschny.de), Aug 01 2009
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