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A196040 Positive integers a for which there is a (4/3)-Pythagorean triple (a,b,c) satisfying a<=b.

%I A196040 #8 Mar 30 2012 18:57:49
%S A196040 7,8,9,11,13,14,15,16,17,18,19,20,20,21,22,23,24,26,27,27,28,28,29,30,
%T A196040 32,33,33,34,35,36,36,39,39,40,40,40,41,42,44,44,45,45,46,47,48,48,49,
%U A196040 51,52,54,54,55,56,56,56,57,58,60,60,63,63,63,63,64,64,66,68
%N A196040 Positive integers a for which there is a (4/3)-Pythagorean triple (a,b,c) satisfying a<=b.
%C A196040 See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.
%t A196040 z8 = 800; z9 = 200; z7 = 200;
%t A196040 k = -4/3; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
%t A196040 d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
%t A196040 t[a_] := Table[d[a, b], {b, a, z8}]
%t A196040 u[n_] := Delete[t[n], Position[t[n], 0]]
%t A196040 Table[u[n], {n, 1, 15}]
%t A196040 t = Table[u[n], {n, 1, z8}];
%t A196040 Flatten[Position[t, {}]]
%t A196040 u = Flatten[Delete[t, Position[t, {}]]];
%t A196040 x[n_] := u[[3 n - 2]];
%t A196040 Table[x[n], {n, 1, z7}]   (* A196033 *)
%t A196040 y[n_] := u[[3 n - 1]];
%t A196040 Table[y[n], {n, 1, z7}]   (* A196034 *)
%t A196040 z[n_] := u[[3 n]];
%t A196040 Table[z[n], {n, 1, z7}]   (* A196035 *)
%t A196040 x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
%t A196040 y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
%t A196040 z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
%t A196040 f = Table[x1[n], {n, 1, z9}];
%t A196040 x2 = Delete[f, Position[f, 0]]   (* A196036 *)
%t A196040 g = Table[y1[n], {n, 1, z9}];
%t A196040 y2 = Delete[g, Position[g, 0]]   (* A196037 *)
%t A196040 h = Table[z1[n], {n, 1, z9}];
%t A196040 z2 = Delete[h, Position[h, 0]]   (* A196038 *)
%Y A196040 Cf. A195770, A196041, A196042, A196043.
%K A196040 nonn
%O A196040 1,1
%A A196040 _Clark Kimberling_, Sep 27 2011