A282346 Least number m > 1 such that the central binomial coefficient C(2m,m) is divisible by m^n.

2, 924, 154836, 227736432, 84331608790, 1138842118714300

Offset: 1

Author

Lucian Craciun and Robert G. Wilson v, Feb 12 2017

Keywords

• nonn
• hard
• more

Comments

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

a(6) <= 4380346834858680. - David A. Corneth, Mar 04 2017

a(7) <= 2404760413443713325. - Giovanni Resta, Mar 16 2017

Links

• Wikipedia, Kummer's theorem.

Crossrefs

Cf. A000108, A000984, A014847, A121943, A282163, A283073, A283074, A282672.

Programs

Mathematica

f[n_] := Block[{k = 2}, While[Mod[Binomial[2k, k], k^n] > 0, k++]; k]

Extensions

a(4)-a(5) from Giovanni Resta, Feb 23 2017

a(6) from Giovanni Resta, Mar 15 2017