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

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, 29, 180, 31, 2, 99, 4, 175, 12, 37, 4, 117, 20, 41, 12, 43, 8, 675, 4, 47, 36, 49, 4, 153, 8, 53, 4, 55, 56, 57, 4, 59, 16

Offset: 0

Author

Peter Luschny, Nov 21 2010

Keywords

• nonn

Links

• Marius A. Burtea, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A170826, A181860, A056040, A000290.

Programs

Magma

[Gcd(n^2, Floor(Factorial(n)/(Factorial(Floor(n/2))^2))):n in [0..60]]; // Marius A. Burtea, Aug 03 2019

Maple

A181861 := n -> igcd(n^2,n!/iquo(n,2)!^2);

Mathematica

sf[n_] := n!/Quotient[n, 2]!^2; Table[GCD[n^2, sf[n]], {n, 0, 60}] (* Jean-François Alcover, Jun 28 2013 *)

PARI

a(n)=gcd(n!/(n\2)!^2,n^2) \\ Charles R Greathouse IV, Feb 01 2013

Formula

a(n) = gcd(A000290(n), A056040(n)).