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A196088 Positive integers a for which there is a (5/3)-Pythagorean triple (a,b,c) satisfying a<=b.

%I A196088 #8 Mar 30 2012 18:57:49
%S A196088 7,9,13,14,15,16,18,19,21,23,25,26,27,27,28,29,30,32,33,35,35,36,39,
%T A196088 40,40,41,42,45,45,45,46,47,48,49,52,53,54,54,55,56,58,59,60,63,63,63,
%U A196088 64,65,69,70,70,71,72,72,75,75,77,80,80,81,81,81,82,83,84,85,87
%N A196088 Positive integers a for which there is a (5/3)-Pythagorean triple (a,b,c) satisfying a<=b.
%C A196088 See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.
%t A196088 z8 = 600; z9 = 150; z7 = 100;
%t A196088 k = 5/3; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
%t A196088 d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
%t A196088 t[a_] := Table[d[a, b], {b, a, z8}]
%t A196088 u[n_] := Delete[t[n], Position[t[n], 0]]
%t A196088 Table[u[n], {n, 1, 15}]
%t A196088 t = Table[u[n], {n, 1, z8}];
%t A196088 Flatten[Position[t, {}]]
%t A196088 u = Flatten[Delete[t, Position[t, {}]]];
%t A196088 x[n_] := u[[3 n - 2]];
%t A196088 Table[x[n], {n, 1, z7}]   (* A196088 *)
%t A196088 y[n_] := u[[3 n - 1]];
%t A196088 Table[y[n], {n, 1, z7}]  (* A196089 *)
%t A196088 z[n_] := u[[3 n]];
%t A196088 Table[z[n], {n, 1, z7}]  (* A196090 *)
%t A196088 x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
%t A196088 y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
%t A196088 z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
%t A196088 f = Table[x1[n], {n, 1, z9}];
%t A196088 x2 = Delete[f, Position[f, 0]]  (* A196091 *)
%t A196088 g = Table[y1[n], {n, 1, z9}];
%t A196088 y2 = Delete[g, Position[g, 0]]  (* A196092 *)
%t A196088 h = Table[z1[n], {n, 1, z9}];
%t A196088 z2 = Delete[h, Position[h, 0]]  (* A196093 *)
%Y A196088 Cf. A195770, A196089, A196090, A196091.
%K A196088 nonn
%O A196088 1,1
%A A196088 _Clark Kimberling_, Sep 27 2011