A082406 Numbers k such that k divides Sum_{j=1..k} binomial(2j,j).

1, 2, 5, 8, 11, 12, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, 107, 113, 130, 131, 137, 149, 167, 173, 179, 191, 196, 197, 227, 233, 238, 239, 251, 257, 263, 266, 269, 281, 293, 311, 317, 322, 347, 353, 359, 383, 389, 401, 419, 431, 443, 449, 461, 467, 479

Offset: 1

Author

Benoit Cloitre, Apr 23 2003

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..4973
• Vaclav Kotesovec, Plot of a(n)/(n*log(n)) for n = 2..10000

Crossrefs

Cf. A066796.

Programs

Mathematica

Select[Range[500],Divisible[Sum[Binomial[2k,k],{k,#}],#]&] (* Harvey P. Dale, Feb 16 2013 *)
A066796 = Accumulate[Table[Binomial[2*k, k], {k, 1, 1000}]]; Select[Range[Length[A066796]], Divisible[A066796[[#]], #] &] (* Vaclav Kotesovec, Feb 15 2019 *)

Formula

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