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 A195925 Positive integers a for which there is a (3/2)-Pythagorean triple (a,b,c) satisfying a<=b. 7

%I

%S 5,6,9,10,12,13,14,15,15,17,18,18,19,20,21,21,22,23,24,25,25,26,27,27,

%T 28,29,30,30,30,30,31,32,33,34,34,35,36,36,38,38,39,39,40,42,42,42,42,

%U 43,44,45,45,45,46,47,48,48,50,50,51,51,52,54,54,54,55,55,56

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

%C See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.

%t z8 = 800; z9 = 400; z7 = 100;

%t k = 3/2; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];

%t d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]

%t t[a_] := Table[d[a, b], {b, a, z8}]

%t u[n_] := Delete[t[n], Position[t[n], 0]]

%t Table[u[n], {n, 1, 15}]

%t t = Table[u[n], {n, 1, z8}];

%t Flatten[Position[t, {}]]

%t u = Flatten[Delete[t, Position[t, {}]]];

%t x[n_] := u[[3 n - 2]];

%t Table[x[n], {n, 1, z7}] (* A195925 *)

%t y[n_] := u[[3 n - 1]];

%t Table[y[n], {n, 1, z7}] (* A195926 *)

%t z[n_] := u[[3 n]];

%t Table[z[n], {n, 1, z7}] (* A195927 *)

%t x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]

%t y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]

%t z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]

%t f = Table[x1[n], {n, 1, z9}];

%t x2 = Delete[f, Position[f, 0]] (* A195928 *)

%t g = Table[y1[n], {n, 1, z9}];

%t y2 = Delete[g, Position[g, 0]] (* A195929 *)

%t h = Table[z1[n], {n, 1, z9}];

%t z2 = Delete[h, Position[h, 0]] (* A195930 *)

%Y (See A195925.)

%K nonn

%O 1,1

%A _Clark Kimberling_, Sep 26 2011

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