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%I #48 Jan 10 2022 05:26:25
%S 2,924,154836,227736432,84331608790,1138842118714300
%N Least number m > 1 such that the central binomial coefficient C(2m,m) is divisible by m^n.
%C Equivalently, least number m > 1 such that the m-th Catalan number C(2m,m)/(m+1) is divisible by m^n. - _Lucian Craciun_, Mar 01 2017
%C a(6) <= 4380346834858680. - _David A. Corneth_, Mar 04 2017
%C a(7) <= 2404760413443713325. - _Giovanni Resta_, Mar 16 2017
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Kummer's_theorem">Kummer's theorem</a>.
%t f[n_] := Block[{k = 2}, While[Mod[Binomial[2k, k], k^n] > 0, k++]; k]
%Y Cf. A000108, A000984, A014847, A121943, A282163, A283073, A283074, A282672.
%K nonn,hard,more
%O 1,1
%A _Lucian Craciun_ and _Robert G. Wilson v_, Feb 12 2017
%E a(4)-a(5) from _Giovanni Resta_, Feb 23 2017
%E a(6) from _Giovanni Resta_, Mar 15 2017
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