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$.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Peter Luschny, Die schwingende Fakultät und Orbitalsysteme, August 2011.
Peter Luschny, Swinging Factorial.
FORMULA
a(n) = rad(n$).
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
KEYWORD
nonn
AUTHOR
Peter Luschny, Aug 02 2009
STATUS
approved