A181859 a(n) = gcd(n^2, n!) / gcd(n^2, n!/floor(n/2)!^2).

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, 169, 27, 98, 1, 5, 1, 512, 11, 289, 7, 108, 1, 361, 13, 80, 1, 147, 1, 242, 3, 529, 1, 64, 49, 625, 17, 338, 1, 729, 55, 56, 57

Offset: 0

Author

Peter Luschny, Nov 21 2010

Keywords

• nonn

Crossrefs

Cf. A170826, A181860, A056040, A000290.

Programs

Maple

A181859 := n -> igcd(n^2,n!)/igcd(n^2,n!/iquo(n,2)!^2);

Mathematica

a[n_] := GCD[n^2, n!]/GCD[n^2, n!/Quotient[n, 2]!^2];
Table[a[n], {n, 0, 57}] (* Jean-François Alcover, Jun 18 2019 *)

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

Formula

a(n) = A170826(n) / A181861(n).