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A163640
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The radical of the swinging factorial A056040 for odd indices.
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1
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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
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OFFSET
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0,2
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COMMENTS
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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)$. It is the largest squarefree divisor of (2*n+1)$, and so also described as the squarefree kernel of (2*n+1)$.
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LINKS
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EXAMPLE
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(2*5+1)$ = 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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MATHEMATICA
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sf[n_] := With[{f = Floor[n/2]}, Pochhammer[f+1, n-f]/f!]; a[n_] := Times @@ FactorInteger[sf[2*n + 1]][[All, 1]]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jul 30 2013 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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