A277913 - OEIS

%I #28 Dec 04 2016 03:55:06

%S 2,3,6,8,12,15,20,24,30,35,42,48,56,60,63,68,72,75,78,80,84,87,90,99,

%T 110,120,132,143,156,168,180,182,195,210,224,240,248,255,264,272,288,

%U 306,312,318,323,330,336,342,360,380,399,420,440,462,483,506,528,552,564,575,588

%N Nonsquare numbers n for which the smallest y>0 solution of the Pellian equation x^2 - n*y^2 = 1 divides n.

%F Lim_{n->infinity} a(n+1)/a(n) = 1 (conjectured).

%e 2 is in the sequence because A002349(2)=2 divides 2.

%e 180 is in the sequence because A002349(180)=12 divides 180.

%t PellSolve[(m_Integer)?Positive] :=

%t   Module[{cf, n, s}, cof = ContinuedFraction[Sqrt[m]];

%t    n = Length[Last[cof]]; If[OddQ[n], n = 2*n];

%t    s = FromContinuedFraction[

%t      ContinuedFraction[Sqrt[m], n]]; {Numerator[s], Denominator[s]}];

%t f[n_] := If[! IntegerQ[Sqrt[n]], PellSolve[n][[2]]];

%t Select[Range[250], Mod[#, f[#]] == 0 &]

%Y See A002349 for the smallest y>0 solution of x^2 - n*y^2 = 1.

%K nonn

%O 1,1

%A _Salvador Cerdá_, Nov 16 2016

%E More terms from _Michel Marcus_, Dec 04 2016