A163640 -id:A163640 - cp's OEIS frontend

A163641 The radical of the swinging factorial A056040.

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

Peter Luschny, Aug 02 2009

nonn

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$.

			11$ = 2772 = 2^2*3^2*7*11. Therefore a(11) = 2*3*7*11 = 462.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Peter Luschny, Die schwingende Fakultät und Orbitalsysteme, August 2011.
Peter Luschny, Swinging Factorial.

Bisections give: A080397 (even part), A163640 (odd part).

Cf. A056040.

a := proc(n) local p; mul(p,p=numtheory[factorset](n!/iquo(n,2)!^2)) end:

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 *)

a(n) = rad(n$).

cp's OEIS Frontend

A163641 The radical of the swinging factorial A056040.

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