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Search: id:A163640
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| A163640 |
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The radical of the swinging factorial A056040 for odd indices. |
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+0
2
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| 1, 6, 30, 70, 210, 462, 6006, 4290, 72930, 461890, 1939938, 4056234, 6760390, 1560090, 6463230, 200360130, 2203961430, 907513530, 33578000610, 22974421470, 941951280270
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Let $ denote the swinging factorial. a(n) is the radical of (2*n+1)$ which is the product of the prime numbers dividing (2*n+1)$. It is the largest square-free divisor of (2*n+1)$, and so also described as the square-free kernel of (2*n+1)$.
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REFERENCES
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Peter Luschny, "Divide, swing and conquer the factorial and the lcm{1,2,...,n}", preprint, April 2008.
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LINKS
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Peter Luschny, Swinging Factorial.
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EXAMPLE
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(2*5+1)$ = 2772 = 2^2*3^2*7*11. Therefore a(5) = 2*3*7*11 = 462.
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MAPLE
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a := proc(n) local p; mul(p, p=numtheory[factorset]((2*n+1)!/iquo(2*n+1, 2)!^2)) end:
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CROSSREFS
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A056040(n) = n$, A163641(n) = rad(n$), A080397(n) = rad((2n)$).
Sequence in context: A145010 A056835 A056836 this_sequence A152743 A038039 A050972
Adjacent sequences: A163637 A163638 A163639 this_sequence A163641 A163642 A163643
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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 02 2009
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