A082406 - OEIS

%I #16 Feb 14 2021 13:01:22

%S 1,2,5,8,11,12,17,23,29,41,47,53,59,71,83,89,101,107,113,130,131,137,

%T 149,167,173,179,191,196,197,227,233,238,239,251,257,263,266,269,281,

%U 293,311,317,322,347,353,359,383,389,401,419,431,443,449,461,467,479

%N Numbers k such that k divides Sum_{j=1..k} binomial(2j,j).

%H Vaclav Kotesovec, <a href="/A082406/b082406.txt">Table of n, a(n) for n = 1..4973</a>

%H Vaclav Kotesovec, <a href="/A082406/a082406.jpg">Plot of a(n)/(n*log(n)) for n = 2..10000</a>

%F Is a(n) asymptotic to c*n*log(n) with 2 < c < 2.3?

%t Select[Range[500],Divisible[Sum[Binomial[2k,k],{k,#}],#]&] (* _Harvey P. Dale_, Feb 16 2013 *)

%t A066796 = Accumulate[Table[Binomial[2*k, k], {k, 1, 1000}]]; Select[Range[Length[A066796]], Divisible[A066796[[#]], #] &] (* _Vaclav Kotesovec_, Feb 15 2019 *)

%Y Cf. A066796.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Apr 23 2003