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A163641
The radical of the swinging factorial A056040.
3
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
OFFSET
0,3
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$.
LINKS
FORMULA
a(n) = rad(n$).
EXAMPLE
11$ = 2772 = 2^2*3^2*7*11. Therefore a(11) = 2*3*7*11 = 462.
MAPLE
a := proc(n) local p; mul(p, p=numtheory[factorset](n!/iquo(n, 2)!^2)) end:
MATHEMATICA
sf[n_] := With[{f = Floor[n/2]}, Pochhammer[f+1, n-f]/f!]; a[0] = 1; a[n_] := Times @@ FactorInteger[sf[n]][[All, 1]]; Table[a[n], {n, 0, 31}] (* Jean-François Alcover, Jul 26 2013 *)
CROSSREFS
Bisections give: A080397 (even part), A163640 (odd part).
Cf. A056040.
Sequence in context: A068629 A144361 A366369 * A333072 A333196 A216850
KEYWORD
nonn
AUTHOR
Peter Luschny, Aug 02 2009
STATUS
approved