A049077 a(n) = n / gcd(n, binomial(n, floor(n/2))).

1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 1, 1, 7, 1, 8, 1, 9, 1, 5, 1, 11, 1, 6, 1, 13, 1, 7, 1, 1, 1, 16, 1, 17, 1, 3, 1, 19, 1, 2, 1, 7, 1, 11, 1, 23, 1, 4, 1, 25, 1, 13, 1, 27, 1, 1, 1, 29, 1, 15, 1, 31, 1, 32, 1, 11, 1, 17, 1, 5, 1, 18, 1, 37, 1, 19, 1, 39, 1, 4, 1, 41, 1, 1, 1, 43, 1, 11, 1, 1, 1, 23

Offset: 1

Author

Labos Elemer, Nov 13 2000

Keywords

• nonn

Examples

			For n = 12, gcd(12, binomial(12, 6)) = gcd(12, 924) = 12, so a(12) = 1.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001405, A057815, A014973.

Programs

Maple

swing := n -> n!/iquo(n,2)!^2: seq(n/igcd(n,swing(n)),n=1..92); # Peter Luschny, May 16 2013

Mathematica

Flatten[Table[{1, n/GCD[n, Binomial[n, n/2]]}, {n, 2, 100, 2}]] (* Alonso del Arte, May 17 2013 *)

PARI

a(n) = n/gcd(n, binomial(n, n\2)); \\ Michel Marcus, Mar 22 2020

Formula

For odd n, a(n) = 1. For even n, a(n) is either n/2 or smaller.

Extensions

Offset changed to 1 by Peter Luschny, May 16 2013