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A163641
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The radical of the swinging factorial A056040.
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2
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1, 1, 2, 6, 6, 30, 10, 70, 70, 210, 42, 462, 462, 6006, 858, 4290, 4290, 72930, 24310, 461890, 92378, 1939938, 176358, 4056234, 1352078, 6760390, 520030, 1560090, 222870, 6463230, 6463230, 200360130
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The radical of n$ is the product of the prime numbers dividing n$. It is the largest squarefree divisor of n$, and so also described as the squarefree kernel of n$.
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REFERENCES
| Peter Luschny, "Divide, swing and conquer the factorial and the lcm{1,2,...,n}", preprint, April 2008.
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LINKS
| Peter Luschny, Swinging Factorial.
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FORMULA
| a(n) = rad(n$)
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EXAMPLE
| 11$ = 2772 = 2^2*3^2*7*11. Therefore a(11) = 2*3*7*11 = 462.
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MAPLE
| a := proc(n) local p; mul(p, p=numtheory[factorset](n!/iquo(n, 2)!^2)) end:
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CROSSREFS
| Cf. A056040, A080397(n) = a(2n), A163640(n) = a(2n+1).
Sequence in context: A077139 A068629 A144361 * A070889 A072744 A056042
Adjacent sequences: A163638 A163639 A163640 * A163642 A163643 A163644
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KEYWORD
| nonn
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AUTHOR
| Peter Luschny (peter(AT)luschny.de), Aug 02 2009
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