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A196001 Positive integers a for which there is a (2/3)-Pythagorean triple (a,b,c) satisfying a<=b.

%I A196001 #8 Mar 30 2012 18:57:49
%S A196001 4,5,7,8,9,10,10,11,12,13,14,15,15,16,16,17,18,18,19,20,20,20,21,21,
%T A196001 22,22,23,24,24,25,25,26,26,27,27,27,28,28,28,29,30,30,30,31,32,32,33,
%U A196001 33,34,34,35,35,35,36,36,36,36,38,38,39,39,40,40,40,41,42,42,42
%N A196001 Positive integers a for which there is a (2/3)-Pythagorean triple (a,b,c) satisfying a<=b.
%C A196001 See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.
%t A196001 z8 = 800; z9 = 400; z7 = 100;
%t A196001 k = 2/3; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
%t A196001 d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
%t A196001 t[a_] := Table[d[a, b], {b, a, z8}]
%t A196001 u[n_] := Delete[t[n], Position[t[n], 0]]
%t A196001 Table[u[n], {n, 1, 15}]
%t A196001 t = Table[u[n], {n, 1, z8}];
%t A196001 Flatten[Position[t, {}]]
%t A196001 u = Flatten[Delete[t, Position[t, {}]]];
%t A196001 x[n_] := u[[3 n - 2]];
%t A196001 Table[x[n], {n, 1, z7}]    (* A196001 *)
%t A196001 y[n_] := u[[3 n - 1]];
%t A196001 Table[y[n], {n, 1, z7}]    (* A196002 *)
%t A196001 z[n_] := u[[3 n]];
%t A196001 Table[z[n], {n, 1, z7}]    (* A196003 *)
%t A196001 x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
%t A196001 y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
%t A196001 z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
%t A196001 f = Table[x1[n], {n, 1, z9}];
%t A196001 x2 = Delete[f, Position[f, 0]]    (* A196004 *)
%t A196001 g = Table[y1[n], {n, 1, z9}];
%t A196001 y2 = Delete[g, Position[g, 0]]    (* A196005 *)
%t A196001 h = Table[z1[n], {n, 1, z9}];
%t A196001 z2 = Delete[h, Position[h, 0]]    (* A196006 *)
%Y A196001 Cf. A195770, A196002, A196003, A196004.
%K A196001 nonn
%O A196001 1,1
%A A196001 _Clark Kimberling_, Sep 26 2011