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%I #22 Aug 02 2019 23:03:14
%S 1,1,1,1,4,1,9,1,32,9,25,1,12,1,49,5,128,1,81,1,100,21,121,1,144,25,
%T 169,27,98,1,5,1,512,11,289,7,108,1,361,13,80,1,147,1,242,3,529,1,64,
%U 49,625,17,338,1,729,55,56,57
%N a(n) = gcd(n^2, n!) / gcd(n^2, n!/floor(n/2)!^2).
%F a(n) = A170826(n) / A181861(n).
%p A181859 := n -> igcd(n^2,n!)/igcd(n^2,n!/iquo(n,2)!^2);
%t a[n_] := GCD[n^2, n!]/GCD[n^2, n!/Quotient[n, 2]!^2];
%t Table[a[n], {n, 0, 57}] (* _Jean-François Alcover_, Jun 18 2019 *)
%o (PARI) a(n)=if(isprime(n), n, if(n==4, 8, n^2))/gcd(n^2,n!/(n\2)!^2) \\ _Charles R Greathouse IV_, Feb 01 2013
%Y Cf. A170826, A181860, A056040, A000290.
%K nonn
%O 0,5
%A _Peter Luschny_, Nov 21 2010
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