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%I #9 Aug 02 2019 21:08:37
%S 69,87,93,159,177,183,249,267,276,312,321,327,348,372,387,417,471,597,
%T 633,636,699,711,717,723,741,747,831,849,879,921,927,987,993,1005,
%U 1068,1104,1137,1179,1248,1251,1272,1293,1299,1317,1320,1353,1359,1383,1392
%N Values k such that singular quadratic unity of Q(k) have gcd(k, y) = 3.
%t cr = {}; ck = {}; Do[If[IntegerQ[Sqrt[n]], , kk = NumberFieldFundamentalUnits[Sqrt[n]]; d1 = kk[[1]][[2]][[1]]; d2 = kk[[1]][[1]] kk[[1]][[2]][[2]]; d4 = Numerator[d2/Sqrt[n]]; If[GCD[d4, n] == 1, , AppendTo[ck, GCD[d4, n]]; AppendTo[cr, n]]], {n, 2, 200000}]; aa = {}; Do[If[ck[[n]] == 3, AppendTo[aa, cr[[n]]]], {n, 1, Length[cr]}]; aa
%Y Cf. A087643, A172000, A194366, A197115, A197127, A197128, A197170, A197171.
%K nonn
%O 2,1
%A _Artur Jasinski_, Oct 11 2011