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A076733 Largest k such that k! divides C(2n,n). 3

%I

%S 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,

%T 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,

%U 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

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

%C All a(n) >= 2, with a(n) = 2 if and only if n is in A005836. - _Robert Israel_, Feb 01 2019

%H Robert Israel, <a href="/A076733/b076733.txt">Table of n, a(n) for n = 1..10000</a>

%p f:= proc(n) local x,k;

%p x:= binomial(2*n,n);

%p for k from 2 do if not (x/k!)::integer then return k-1 fi od

%p end proc:

%p map(f, [$1..105]); # _Robert Israel_, Feb 01 2019

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

%Y Cf. A005836, A055881.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Oct 28 2002

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Last modified May 13 08:08 EDT 2021. Contains 343836 sequences. (Running on oeis4.)