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

%I A266969 #23 May 12 2024 00:46:50
%S A266969 1,2,21,266,387,657,1314,6291,16113,25767,27594,41902,54243,55314,
%T A266969 56457,89018,96141,155601,172746,219842,294273,300871,384426,412398,
%U A266969 453781,579474,653421,660879,669609,951881,993307,1117338,1246077,1401258,1438623,1535409,1870533
%N A266969 Integers k such that A001006(k) is divisible by k.
%C A266969 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.
%C A266969 Corresponding values of A001006(n)/n are 1, 1, 6787979, ...
%H A266969 Amiram Eldar, <a href="/A266969/b266969.txt">Table of n, a(n) for n = 1..70</a>
%e A266969 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.
%t A266969 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 *)
%t A266969 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 *)
%o A266969 (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
%Y A266969 Cf. A001006, A081735.
%K A266969 nonn
%O A266969 1,2
%A A266969 _Altug Alkan_, Jan 07 2016
%E A266969 a(8)-a(17) from _Michael De Vlieger_, Jan 09 2016
%E A266969 a(18)-a(37) from _Amiram Eldar_, May 12 2024