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A282346 Least number m > 1 such that the central binomial coefficient C(2m,m) is divisible by m^n. 6
2, 924, 154836, 227736432, 84331608790, 1138842118714300 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

Table of n, a(n) for n=1..6.

Wikipedia, Kummer's theorem.

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A265617 A324597 A159723 * A070967 A070927 A070922

Adjacent sequences:  A282343 A282344 A282345 * A282347 A282348 A282349

KEYWORD

nonn,hard,more

AUTHOR

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

EXTENSIONS

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

a(6) from Giovanni Resta, Mar 15 2017

STATUS

approved

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Last modified May 28 18:07 EDT 2022. Contains 354120 sequences. (Running on oeis4.)