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A277913 Nonsquare numbers n for which the smallest y>0 solution of the Pellian equation x^2 - n*y^2 = 1 divides n. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 14 01:29 EDT 2020. Contains 336473 sequences. (Running on oeis4.)