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A266969
Integers k such that A001006(k) is divisible by k.
18
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
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
Sequence in context: A105712 A087677 A374675 * A229036 A097627 A094797
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