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A196098 Positive integers a for which there is a (5/4)-Pythagorean triple (a,b,c) satisfying a<=b.

%I A196098 #8 Mar 30 2012 18:57:49
%S A196098 3,4,6,8,9,10,11,12,12,14,15,15,16,17,18,19,20,20,20,21,22,22,23,24,
%T A196098 24,25,26,27,28,28,28,29,30,30,30,31,32,32,33,33,33,34,35,35,36,36,36,
%U A196098 37,38,39,40,40,40,42,42,42,44,44,44,45,45,46,47,48,48,50,51,51
%N A196098 Positive integers a for which there is a (5/4)-Pythagorean triple (a,b,c) satisfying a<=b.
%C A196098 See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.
%t A196098 z8 = 600; z9 = 150; z7 = 100;
%t A196098 k = 5/3; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
%t A196098 d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
%t A196098 t[a_] := Table[d[a, b], {b, a, z8}]
%t A196098 u[n_] := Delete[t[n], Position[t[n], 0]]
%t A196098 Table[u[n], {n, 1, 15}]
%t A196098 t = Table[u[n], {n, 1, z8}];
%t A196098 Flatten[Position[t, {}]]
%t A196098 u = Flatten[Delete[t, Position[t, {}]]];
%t A196098 x[n_] := u[[3 n - 2]];
%t A196098 Table[x[n], {n, 1, z7}]  (* A196088 *)
%t A196098 y[n_] := u[[3 n - 1]];
%t A196098 Table[y[n], {n, 1, z7}]  (* A196089 *)
%t A196098 z[n_] := u[[3 n]];
%t A196098 Table[z[n], {n, 1, z7}]  (* A196090 *)
%t A196098 x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
%t A196098 y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
%t A196098 z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
%t A196098 f = Table[x1[n], {n, 1, z9}];
%t A196098 x2 = Delete[f, Position[f, 0]]  (* A196091 *)
%t A196098 g = Table[y1[n], {n, 1, z9}];
%t A196098 y2 = Delete[g, Position[g, 0]]  (* A196092 *)
%t A196098 h = Table[z1[n], {n, 1, z9}];
%t A196098 z2 = Delete[h, Position[h, 0]]  (* A196093 *)
%Y A196098 Cf. A195770, A196097, A196099, A196100, A196101.
%K A196098 nonn
%O A196098 1,1
%A A196098 _Clark Kimberling_, Sep 28 2011