A110499 - OEIS

%I #2 Mar 30 2012 17:22:40

%S 4,1056,540928

%N Largest k such that n is the highest power in the factorization of binomial(2k,k).

%C Checked all k < 10^8. a(1) has been proved. a(2) and a(3) are conjectured.

%C Checked all k < 10^9. a(4) is at least 537927682. - _T. D. Noe_, Jul 27 2005

%e a(1)=4 because binomial(8,4) is the largest squarefree central binomial coefficient. a(2)=1056 because binomial(2112,1056) is the largest cubefree.

%Y Cf. A110495 (n such that binomial(2n, n) is cubefree).

%K bref,nonn

%O 1,1

%A _T. D. Noe_, Jul 22 2005