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

1,2

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, ...

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A001006, A081735.

Sequence in context: A045726 A105712 A087677 * A229036 A097627 A094797

Adjacent sequences: A266966 A266967 A266968 * A266970 A266971 A266972

Keyword

nonn

Author

Altug Alkan, Jan 07 2016

Extensions

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

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

Status

approved