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A195932 Positive integers a for which there is a (-1/3)-Pythagorean triple (a,b,c) satisfying a<=b. 7

%I

%S 1,2,3,4,5,6,7,7,8,8,9,9,9,9,10,11,11,12,13,13,13,14,14,15,15,15,16,

%T 16,16,16,17,17,17,18,18,18,18,19,19,20,21,21,21,22,22,23,23,23,24,24,

%U 24,24,25,25,26,26,27,27,27,27,27,27,27,28,28,29,29,29,30,30,30

%N Positive integers a for which there is a (-1/3)-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 = -1/3; 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}] (* A195932 *)

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

%t Table[y[n], {n, 1, z7}] (* A195933 *)

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

%t Table[z[n], {n, 1, z7}] (* A195934 *)

%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]] (* A195935 *)

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

%t y2 = Delete[g, Position[g, 0]] (* A195936 *)

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

%t z2 = Delete[h, Position[h, 0]] (* A195937 *)

%Y Cf. A195770, A195933, A195934, A195935.

%K nonn

%O 1,2

%A _Clark Kimberling_, Sep 26 2011

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Last modified January 29 04:57 EST 2020. Contains 331335 sequences. (Running on oeis4.)