A071416 a(n) = gcd(n, binomial(2*n, n)).

1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 4, 1, 2, 15, 2, 1, 6, 1, 20, 3, 2, 1, 12, 1, 2, 1, 28, 1, 2, 1, 2, 3, 2, 7, 4, 1, 2, 1, 20, 1, 42, 1, 4, 45, 2, 1, 12, 1, 2, 3, 4, 1, 6, 1, 8, 3, 2, 1, 12, 1, 2, 3, 2, 5, 66, 1, 4, 3, 10, 1, 36, 1, 2, 15, 4, 77, 6, 1, 20, 1, 2, 1, 28, 5, 2, 3, 88, 1, 10, 91, 4, 1, 2, 5

Offset: 1

Author

Reinhard Zumkeller, May 29 2002

Keywords

• nonn
• nice

Comments

a(n) = n for n in A014847. - Reinhard Zumkeller

a(n) = gcd(n, C(n)), C(n) the Catalan numbers. - Peter Luschny Oct 06 2011

Examples

			a(10) = gcd(10, binomial(20, 10)) = gcd(10, 184756) = 2.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Central Binomial Coefficient

Crossrefs

Cf. A000984, A000108.

Programs

Mathematica

Table[GCD[n,Binomial[2n,n]],{n,100}] (* Harvey P. Dale, Nov 10 2011 *)