A197172 Values k such that singular quadratic unity of Q(k) have gcd(k, y) = 3.
69, 87, 93, 159, 177, 183, 249, 267, 276, 312, 321, 327, 348, 372, 387, 417, 471, 597, 633, 636, 699, 711, 717, 723, 741, 747, 831, 849, 879, 921, 927, 987, 993, 1005, 1068, 1104, 1137, 1179, 1248, 1251, 1272, 1293, 1299, 1317, 1320, 1353, 1359, 1383, 1392
Offset: 2
Keywords
Programs
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Mathematica
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