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A181861 a(n) = gcd(n^2, n!/floor(n/2)!^2).

%I A181861 #20 Sep 08 2022 08:45:54
%S A181861 1,1,2,3,2,5,4,7,2,9,4,11,12,13,4,45,2,17,4,19,4,21,4,23,4,25,4,27,8,
%T A181861 29,180,31,2,99,4,175,12,37,4,117,20,41,12,43,8,675,4,47,36,49,4,153,
%U A181861 8,53,4,55,56,57,4,59,16
%N A181861 a(n) = gcd(n^2, n!/floor(n/2)!^2).
%H A181861 Marius A. Burtea, <a href="/A181861/b181861.txt">Table of n, a(n) for n = 0..1000</a>
%F A181861 a(n) = gcd(A000290(n), A056040(n)).
%p A181861 A181861 := n -> igcd(n^2,n!/iquo(n,2)!^2);
%t A181861 sf[n_] := n!/Quotient[n, 2]!^2; Table[GCD[n^2, sf[n]], {n, 0, 60}] (* _Jean-François Alcover_, Jun 28 2013 *)
%o A181861 (PARI) a(n)=gcd(n!/(n\2)!^2,n^2) \\ _Charles R Greathouse IV_, Feb 01 2013
%o A181861 (Magma) [Gcd(n^2, Floor(Factorial(n)/(Factorial(Floor(n/2))^2))):n in [0..60]]; // _Marius A. Burtea_, Aug 03 2019
%Y A181861 Cf. A170826, A181860, A056040, A000290.
%K A181861 nonn
%O A181861 0,3
%A A181861 _Peter Luschny_, Nov 21 2010