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Number of k, 1<=k<=n, such that C(n,k) divides C(2n,2k).
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%I #7 Jul 10 2012 16:31:45

%S 1,2,3,3,5,5,3,7,7,5,7,5,7,11,9,3,5,13,9,13,7,3,11,9,7,9,7,11,11,9,3,

%T 9,23,13,19,9,3,7,11,7,11,9,9,9,7,7,5,19,13,23,15,7,17,13,9,7,5,5,7,

%U 11,11,11,19,11,15,9,11,21,19,11,9,9,9,13,11,5,13,21,9,11,15,7,13,9,7,11,7,15

%N Number of k, 1<=k<=n, such that C(n,k) divides C(2n,2k).

%C Is a(n) odd for n>2 ? All odd numbers occur? Does equation a(x)=2m+1 have infinitely many solutions for any m>=1?

%H Harvey P. Dale, <a href="/A081768/b081768.txt">Table of n, a(n) for n = 1..1000</a>

%t Total/@Table[If[Divisible[Binomial[2n,2k],Binomial[n,k]],1,0], {n,90}, {k,n}] (* _Harvey P. Dale_, Jul 10 2012 *)

%K easy,nonn

%O 1,2

%A _Benoit Cloitre_, Apr 09 2003