A266969 Integers k such that A001006(k) is divisible by k.

1, 2, 21, 266, 387, 657, 1314, 6291, 16113, 25767, 27594, 41902, 54243, 55314, 56457, 89018, 96141, 155601, 172746, 219842, 294273, 300871, 384426, 412398, 453781, 579474, 653421, 660879, 669609, 951881, 993307, 1117338, 1246077, 1401258, 1438623, 1535409, 1870533

Offset: 1

Author

Altug Alkan, Jan 07 2016

Keywords

• nonn

Comments

Integers n such that number of ways of drawing any number of nonintersecting chords joining n (labeled) points on a circle is divisible by n.

Corresponding values of A001006(n)/n are 1, 1, 6787979, ...

Examples

			There are 142547559 ways to join 21 points on a circle by nonintersecting chords. Because of the fact that 142547559 is divisible by 21, 21 is a term of this sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..70

Crossrefs

Cf. A001006, A081735.

Programs

Mathematica

lim = 100000; t = CoefficientList[Series[(1 - x - (1 - 2 x - 3 x^2)^(1/2))/(2 x^2), {x, 0, lim}], x]; Select[Range@ lim, Divisible[t[[# + 1]], #] &] (* Michael De Vlieger, Jan 09 2016, after Jean-François Alcover at A001006 *)
seq[kmax_] := Module[{mot1 = 1, mot2 = 2, mot, s = {1, 2}}, Do[mot3 = ((2*k+1)*mot2 + (3*k-3)*mot1)/(k+2); If[Divisible[mot3, k], AppendTo[s, k]]; mot1 = mot2; mot2 = mot3, {k, 3, kmax}]; s]; seq[10^5] (* Amiram Eldar, May 12 2024 *)

PARI

lista(kmax) = {my(mot1 = 1, mot2 = 2, mot); print1(1, ", ", 2, ", "); for(k = 3, kmax, mot3 = ((2*k+1)*mot2 + (3*k-3)*mot1)/(k+2); if(!(mot3 % k), print1(k,", ")); mot1 = mot2; mot2 = mot3);} \\ Amiram Eldar, May 12 2024

Extensions

a(8)-a(17) from Michael De Vlieger, Jan 09 2016

a(18)-a(37) from Amiram Eldar, May 12 2024