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A163641 The radical of the swinging factorial A056040. 2
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 (list; graph; refs; listen; history; text; internal format)
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$.

REFERENCES

Peter Luschny, "Divide, swing and conquer the factorial and the lcm{1,2,...,n}", preprint, April 2008.

LINKS

Table of n, a(n) for n=0..31.

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-Fran├žois Alcover, Jul 26 2013 *)

CROSSREFS

Cf. A056040, A080397(n) = a(2n), A163640(n) = a(2n+1).

Sequence in context: A077139 A068629 A144361 * A216850 A070889 A072744

Adjacent sequences:  A163638 A163639 A163640 * A163642 A163643 A163644

KEYWORD

nonn

AUTHOR

Peter Luschny, Aug 02 2009

STATUS

approved

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Last modified May 23 16:30 EDT 2017. Contains 286925 sequences.