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A196162 Positive integers a for which there is a 6-Pythagorean triple (a,b,c) satisfying a<=b.

%I A196162 #8 Mar 30 2012 18:57:49
%S A196162 2,3,4,4,5,5,6,6,6,7,7,8,8,8,9,9,9,10,10,10,10,11,11,12,12,12,12,12,
%T A196162 13,13,14,14,14,14,14,15,15,15,15,15,16,16,16,16,17,17,18,18,18,18,18,
%U A196162 18,18,19,19,20,20,20,20,20,20,21,21,21,21,21,21,22,22,22,22,23
%N A196162 Positive integers a for which there is a 6-Pythagorean triple (a,b,c) satisfying a<=b.
%C A196162 See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.
%t A196162 z8 = 900; z9 = 250; z7 = 200;
%t A196162 k = 6; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
%t A196162 d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
%t A196162 t[a_] := Table[d[a, b], {b, a, z8}]
%t A196162 u[n_] := Delete[t[n], Position[t[n], 0]]
%t A196162 Table[u[n], {n, 1, 15}]
%t A196162 t = Table[u[n], {n, 1, z8}];
%t A196162 Flatten[Position[t, {}]]
%t A196162 u = Flatten[Delete[t, Position[t, {}]]];
%t A196162 x[n_] := u[[3 n - 2]];
%t A196162 Table[x[n], {n, 1, z7}]  (* A196162 *)
%t A196162 y[n_] := u[[3 n - 1]];
%t A196162 Table[y[n], {n, 1, z7}]  (* A196163 *)
%t A196162 z[n_] := u[[3 n]];
%t A196162 Table[z[n], {n, 1, z7}]  (* A196164 *)
%t A196162 x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
%t A196162 y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
%t A196162 z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
%t A196162 f = Table[x1[n], {n, 1, z9}];
%t A196162 x2 = Delete[f, Position[f, 0]]  (* A196165 *)
%t A196162 g = Table[y1[n], {n, 1, z9}];
%t A196162 y2 = Delete[g, Position[g, 0]]  (* A196166 *)
%t A196162 h = Table[z1[n], {n, 1, z9}];
%t A196162 z2 = Delete[h, Position[h, 0]]  (* A196167 *)
%Y A196162 Cf. A195770, A196163, A196164, A196165.
%K A196162 nonn
%O A196162 1,1
%A A196162 _Clark Kimberling_, Sep 28 2011