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A196390 Positive integers a for which there is a (-6)-Pythagorean triple (a,b,c) satisfying a<=b.

%I A196390 #10 Mar 30 2012 18:57:50
%S A196390 1,2,2,3,3,3,4,4,4,5,5,5,6,6,6,6,6,6,7,7,7,8,8,8,8,9,9,9,9,9,10,10,10,
%T A196390 10,10,10,11,11,11,12,12,12,12,12,12,12,12,12,13,13,13,14,14,14,14,14,
%U A196390 14,15,15,15,15,15,15,15,15,15,16,16,16,16,16,17,17,17,18,18,18,18,18,18,18,18,18,18,19,19,19,20,20,20,20,20,20,20,20,20,21,21
%N A196390 Positive integers a for which there is a (-6)-Pythagorean triple (a,b,c) satisfying a<=b.
%C A196390 See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.
%t A196390 z8 = 900; z9 = 250; z7 = 200;
%t A196390 pIntegerQ := IntegerQ[#1] && #1 > 0 &;
%t A196390 k = -6; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
%t A196390 d[a_, b_] := If[pIntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
%t A196390 t[a_] := Table[d[a, b], {b, a, z8}]
%t A196390 u[n_] := Delete[t[n], Position[t[n], 0]]
%t A196390 Table[u[n], {n, 1, 15}]
%t A196390 t = Table[u[n], {n, 1, z8}];
%t A196390 Flatten[Position[t, {}]]
%t A196390 u = Flatten[Delete[t, Position[t, {}]]];
%t A196390 x[n_] := u[[3 n - 2]];
%t A196390 Table[x[n], {n, 1, z7}]  (* A196390 *)
%t A196390 y[n_] := u[[3 n - 1]];
%t A196390 Table[y[n], {n, 1, z7}]  (* A196391 *)
%t A196390 z[n_] := u[[3 n]];
%t A196390 Table[z[n], {n, 1, z7}]  (* A196392 *)
%t A196390 x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
%t A196390 y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
%t A196390 z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
%t A196390 f = Table[x1[n], {n, 1, z9}];
%t A196390 x2 = Delete[f, Position[f, 0]]  (* A196393 *)
%t A196390 g = Table[y1[n], {n, 1, z9}];
%t A196390 y2 = Delete[g, Position[g, 0]]  (* A196394 *)
%t A196390 h = Table[z1[n], {n, 1, z9}];
%t A196390 z2 = Delete[h, Position[h, 0]]  (* A196395 *)
%Y A196390 Cf. A195770, A196391, A196392, A196393.
%K A196390 nonn
%O A196390 1,2
%A A196390 _Clark Kimberling_, Oct 01 2011