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

Author

Benoit Cloitre, Oct 28 2002

Keywords

• nonn

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

Crossrefs

Cf. A005836, A055881.

Programs

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 *)

PARI

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