This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A163641 #17 Aug 22 2025 04:01:32
%S A163641 1,1,2,6,6,30,10,70,70,210,42,462,462,6006,858,4290,4290,72930,24310,
%T A163641 461890,92378,1939938,176358,4056234,1352078,6760390,520030,1560090,
%U A163641 222870,6463230,6463230,200360130
%N A163641 The radical of the swinging factorial A056040.
%C A163641 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$.
%H A163641 G. C. Greubel, <a href="/A163641/b163641.txt">Table of n, a(n) for n = 0..1000</a>
%H A163641 Peter Luschny, <a href="/A180000/a180000.pdf">Die schwingende Fakultät und Orbitalsysteme</a>, August 2011.
%H A163641 Peter Luschny, <a href="http://www.luschny.de/math/swing/SwingingFactorial.html">Swinging Factorial</a>.
%F A163641 a(n) = rad(n$).
%e A163641 11$ = 2772 = 2^2*3^2*7*11. Therefore a(11) = 2*3*7*11 = 462.
%p A163641 a := proc(n) local p; mul(p,p=numtheory[factorset](n!/iquo(n,2)!^2)) end:
%t A163641 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 *)
%Y A163641 Bisections give: A080397 (even part), A163640 (odd part).
%Y A163641 Cf. A056040.
%K A163641 nonn
%O A163641 0,3
%A A163641 _Peter Luschny_, Aug 02 2009