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A277913
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Nonsquare numbers n for which the smallest y>0 solution of the Pellian equation x^2 - n*y^2 = 1 divides n.
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0
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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
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OFFSET
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1,1
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LINKS
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FORMULA
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Lim_{n->infinity} a(n+1)/a(n) = 1 (conjectured).
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EXAMPLE
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2 is in the sequence because A002349(2)=2 divides 2.
180 is in the sequence because A002349(180)=12 divides 180.
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MATHEMATICA
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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 &]
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CROSSREFS
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See A002349 for the smallest y>0 solution of x^2 - n*y^2 = 1.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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