A277913 Nonsquare numbers n for which the smallest y>0 solution of the Pellian equation x^2 - n*y^2 = 1 divides n.

2, 3, 6, 8, 12, 15, 20, 24, 30, 35, 42, 48, 56, 60, 63, 68, 72, 75, 78, 80, 84, 87, 90, 99, 110, 120, 132, 143, 156, 168, 180, 182, 195, 210, 224, 240, 248, 255, 264, 272, 288, 306, 312, 318, 323, 330, 336, 342, 360, 380, 399, 420, 440, 462, 483, 506, 528, 552, 564, 575, 588

Offset

1,1

Links

Table of n, a(n) for n=1..61.

Formula

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

Example

2 is in the sequence because A002349(2)=2 divides 2.
180 is in the sequence because A002349(180)=12 divides 180.

Mathematica

PellSolve[(m_Integer)?Positive] :=
  Module[{cf, n, s}, cof = ContinuedFraction[Sqrt[m]];
   n = Length[Last[cof]]; If[OddQ[n], n = 2*n];
   s = FromContinuedFraction[
     ContinuedFraction[Sqrt[m], n]]; {Numerator[s], Denominator[s]}];
f[n_] := If[! IntegerQ[Sqrt[n]], PellSolve[n][[2]]];
Select[Range[250], Mod[#, f[#]] == 0 &]

Crossrefs

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

Sequence in context: A098393 A263883 A103567 * A131723 A198442 A035106

Adjacent sequences: A277910 A277911 A277912 * A277914 A277915 A277916

Keyword

nonn

Author

Salvador Cerdá, Nov 16 2016

Extensions

More terms from Michel Marcus, Dec 04 2016

Status

approved