A248123 Least integer m > 0 such that gcd(m,n) = 1 and m*n | C(m+n), where C(k) refers to the k-th Catalan number binomial(2k,k)/(k+1).

1, 3, 2, 21, 9, 11, 11, 77, 5, 13, 6, 85, 10, 5, 1, 77, 11, 5, 11, 1, 4, 7, 13, 29, 18, 7, 14, 1, 15, 11, 17, 189, 19, 9, 6, 5, 23, 15, 7, 49, 23, 1, 22, 17, 1, 13, 25, 13, 26, 19, 11, 9, 28, 71, 18, 29, 10, 15, 31, 13, 34, 17, 5, 381, 9, 1, 35, 9, 19, 9

Offset: 1

Author

Zhi-Wei Sun, Oct 01 2014

Keywords

• nonn

Comments

Conjecture: a(n) exists for all n > 0.

Examples

			a(4) = 21 since 4*21 divides C(4+21) = 4861946401452.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000108, A248058, A248124.

Programs

Mathematica

Do[m=1;Label[aa];If[GCD[m,n]==1&&Mod[CatalanNumber[m+n],m*n]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,70}]