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A195872 Positive integers a for which there is a (-1/2)-Pythagorean triple (a,b,c) satisfying a<=b.

%I A195872 #8 Mar 30 2012 18:57:48
%S A195872 1,2,3,4,5,5,6,6,6,7,7,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13,13,14,
%T A195872 14,14,14,15,15,15,16,16,16,17,17,17,18,18,18,18,18,19,19,19,20,20,20,
%U A195872 21,21,21,22,22,22,22,22,23,23,23,24,24,24,25,25,26,26,26,26
%N A195872 Positive integers a for which there is a (-1/2)-Pythagorean triple (a,b,c) satisfying a<=b.
%C A195872 See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.
%e A195872 (-1/2)-Pythagorean triples:
%e A195872 1,2,2
%e A195872 2,4,4
%e A195872 3,6,6
%e A195872 4,8,8
%e A195872 5,48,47
%e A195872 (For primitive triples, see A195875.)
%t A195872 z8 = 800; z9 = 400; z7 = 100;
%t A195872 k = -1/2; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
%t A195872 d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
%t A195872 t[a_] := Table[d[a, b], {b, a, z8}]
%t A195872 u[n_] := Delete[t[n], Position[t[n], 0]]
%t A195872 Table[u[n], {n, 1, 15}]
%t A195872 t = Table[u[n], {n, 1, z8}];
%t A195872 Flatten[Position[t, {}]]
%t A195872 u = Flatten[Delete[t, Position[t, {}]]];
%t A195872 x[n_] := u[[3 n - 2]];
%t A195872 Table[x[n], {n, 1, z7}]    (* A195872 *)
%t A195872 y[n_] := u[[3 n - 1]];
%t A195872 Table[y[n], {n, 1, z7}]    (* A195873 *)
%t A195872 z[n_] := u[[3 n]];
%t A195872 Table[z[n], {n, 1, z7}]    (* A195874 *)
%t A195872 x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
%t A195872 y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
%t A195872 z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
%t A195872 f = Table[x1[n], {n, 1, z9}];
%t A195872 x2 = Delete[f, Position[f, 0]]    (* A195875 *)
%t A195872 g = Table[y1[n], {n, 1, z9}];
%t A195872 y2 = Delete[g, Position[g, 0]]    (* A195876 *)
%t A195872 h = Table[z1[n], {n, 1, z9}];
%t A195872 z2 = Delete[h, Position[h, 0]]    (* A195877 *)
%Y A195872 Cf. A195770, A195875.
%K A195872 nonn
%O A195872 1,2
%A A195872 _Clark Kimberling_, Sep 25 2011