A076733 Largest k such that k! divides C(2n,n).

2, 3, 2, 2, 3, 3, 4, 3, 2, 2, 4, 2, 2, 5, 6, 3, 3, 3, 5, 3, 5, 5, 6, 3, 4, 4, 2, 2, 5, 2, 2, 3, 3, 3, 4, 2, 2, 5, 2, 2, 5, 5, 7, 5, 7, 7, 7, 3, 5, 4, 4, 4, 7, 5, 4, 4, 4, 5, 6, 4, 4, 4, 5, 3, 3, 3, 5, 3, 5, 5, 6, 3, 5, 5, 7, 5, 7, 7, 7, 3, 2, 2, 5, 2, 2, 7, 5, 5, 7, 2, 2, 5, 2, 2, 7, 3, 5, 5, 5, 5, 6, 5, 5, 5, 6

Offset

1,1

Comments

All a(n) >= 2, with a(n) = 2 if and only if n is in A005836. - Robert Israel, Feb 01 2019

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

f:= proc(n) local x, k;
  x:= binomial(2*n, n);
  for k from 2 do if not (x/k!)::integer then return k-1 fi od
end proc:
map(f, [$1..105]); # Robert Israel, Feb 01 2019

Mathematica

a[n_] := Module[{k = 2}, While[Divisible[Binomial[2n, n], k!], k++]; k-1];
Table[a[n], {n, 1, 105}] (* Jean-François Alcover, Oct 01 2024 *)

Prog

(PARI) a(n)=if(n<0, 0, k=1; while(binomial(2*n, n)%(k!) == 0, k++); k-1)

Crossrefs

Cf. A005836, A055881.

Sequence in context: A242789 A366712 A366713 * A079643 A329317 A118480

Adjacent sequences: A076730 A076731 A076732 * A076734 A076735 A076736

Keyword

nonn

Author

Benoit Cloitre, Oct 28 2002

Status

approved