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

0,3

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

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

Cf. A056040.

Sequence in context: A068629 A144361 A366369 * A333072 A333196 A216850

Adjacent sequences: A163638 A163639 A163640 * A163642 A163643 A163644

Keyword

nonn

Author

Peter Luschny, Aug 02 2009

Status

approved