cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 216 results. Next

A196026 Positive integers a for which there is a (5/2)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

5, 6, 7, 9, 10, 11, 12, 13, 14, 14, 15, 16, 17, 18, 18, 19, 20, 21, 21, 22, 22, 23, 24, 25, 25, 25, 26, 26, 27, 28, 28, 29, 30, 30, 30, 31, 32, 32, 33, 34, 34, 35, 35, 35, 36, 36, 37, 38, 38, 38, 39, 40, 41, 42, 42, 42, 43, 44, 44, 45, 45, 46, 46, 47, 48, 48, 48, 49
Offset: 1

Views

Author

Clark Kimberling, Sep 26 2011

Keywords

Comments

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

Crossrefs

Cf. A195770, A196027, A106028, A196029.

Programs

  • Mathematica
    z8 = 800; z9 = 150; z7 = 100;
k = 5/2; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
t[a_] := Table[d[a, b], {b, a, z8}]
u[n_] := Delete[t[n], Position[t[n], 0]]
Table[u[n], {n, 1, 15}]
t = Table[u[n], {n, 1, z8}];
Flatten[Position[t, {}]]
u = Flatten[Delete[t, Position[t, {}]]];
x[n_] := u[[3 n - 2]];
Table[x[n], {n, 1, z7}]   (* A196026 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]   (* A196027 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]   (* A196028 *)
x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
f = Table[x1[n], {n, 1, z9}];
x2 = Delete[f, Position[f, 0]]   (* A196029 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]   (* A196030 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]   (* A196031 *)

A195778 Positive integers a for which there is a (-1)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

1, 2, 3, 3, 4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 24, 24, 25, 25, 25
Offset: 1

Views

Author

Clark Kimberling, Sep 25 2011

Keywords

Comments

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

Examples

			First five (-1)-Pythagorean triples (A195778):
(1,1,1), (2,2,2), (3,3,3), (3,8,7), (4,4,4).
First five primitive (-1)-Pythagorean triples (A195796):
(1,1,1), (3,8,7), (5,8,7), (5,21,19), (7,15,13).

Crossrefs

Cf. A195770, A009004, A195794, A195795, A195796, A195862, A195863.

Programs

  • Mathematica
    z8 = 800; z9 = 400; z7 = 100;
k = -1; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
t[a_] := Table[d[a, b], {b, a, z8}]
u[n_] := Delete[t[n], Position[t[n], 0]]
Table[u[n], {n, 1, 15}]
t = Table[u[n], {n, 1, z8}];
Flatten[Position[t, {}]]
u = Flatten[Delete[t, Position[t, {}]]];
x[n_] := u[[3 n - 2]];
Table[x[n], {n, 1, z7}]  (* A195778 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]  (* A195794 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]  (* A195795 *)
x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
f = Table[x1[n], {n, 1, z9}];
x2 = Delete[f, Position[f, 0]] (* A195796 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]] (* A195862 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]] (* A195863 *)

A195939 Positive integers a for which there is a (1/3)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

3, 5, 5, 6, 7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 12, 13, 14, 15, 15, 15, 16, 16, 16, 17, 18, 18, 18, 19, 19, 20, 20, 21, 21, 21, 22, 22, 23, 24, 24, 24, 25, 25, 26, 27, 27, 27, 27, 27, 27, 28, 29, 30, 30, 30, 31, 31, 32, 32, 32, 32, 32, 33, 33, 33, 34, 35, 35, 35, 36, 36
Offset: 1

Views

Author

Clark Kimberling, Sep 26 2011

Keywords

Comments

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

Crossrefs

Cf. A195770, A195940, A195941, A195990.

Programs

  • Mathematica
    z8 = 800; z9 = 400; z7 = 100;
k = 1/3; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
t[a_] := Table[d[a, b], {b, a, z8}]
u[n_] := Delete[t[n], Position[t[n], 0]]
Table[u[n], {n, 1, 15}]
t = Table[u[n], {n, 1, z8}];
Flatten[Position[t, {}]]
u = Flatten[Delete[t, Position[t, {}]]];
x[n_] := u[[3 n - 2]];
Table[x[n], {n, 1, z7}]  (* A195939 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]  (* A195940 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]  (* A195941 *)
x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
f = Table[x1[n], {n, 1, z9}];
x2 = Delete[f, Position[f, 0]] (* A195990 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]] (* A195991 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]] (* A195992 *)

A196033 Positive integers a for which there is a (-4/3)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

3, 4, 5, 6, 7, 8, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 15, 16, 16, 16, 17, 18, 18, 19, 20, 20, 21, 21, 21, 22, 23, 24, 24, 24, 24, 25, 26, 27, 27, 27, 27, 28, 28, 28, 28, 29, 30, 30, 31, 32, 32, 32, 32, 33, 33, 33, 34, 35, 35, 35, 36, 36, 36, 36, 36, 36, 37, 38, 39
Offset: 1

Views

Author

Clark Kimberling, Sep 27 2011

Keywords

Comments

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

Crossrefs

Cf. A195770, A196034, A196035, A196036.

Programs

  • Mathematica
    z8 = 800; z9 = 200; z7 = 200;
k = -4/3; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
t[a_] := Table[d[a, b], {b, a, z8}]
u[n_] := Delete[t[n], Position[t[n], 0]]
Table[u[n], {n, 1, 15}]
t = Table[u[n], {n, 1, z8}];
Flatten[Position[t, {}]]
u = Flatten[Delete[t, Position[t, {}]]];
x[n_] := u[[3 n - 2]];
Table[x[n], {n, 1, z7}]   (* A196033 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]   (* A196034 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]   (* A196035 *)
x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
f = Table[x1[n], {n, 1, z9}];
x2 = Delete[f, Position[f, 0]]   (* A196036 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]   (* A196037 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]   (* A196038 *)

A196088 Positive integers a for which there is a (5/3)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

7, 9, 13, 14, 15, 16, 18, 19, 21, 23, 25, 26, 27, 27, 28, 29, 30, 32, 33, 35, 35, 36, 39, 40, 40, 41, 42, 45, 45, 45, 46, 47, 48, 49, 52, 53, 54, 54, 55, 56, 58, 59, 60, 63, 63, 63, 64, 65, 69, 70, 70, 71, 72, 72, 75, 75, 77, 80, 80, 81, 81, 81, 82, 83, 84, 85, 87
Offset: 1

Views

Author

Clark Kimberling, Sep 27 2011

Keywords

Comments

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

Crossrefs

Cf. A195770, A196089, A196090, A196091.

Programs

  • Mathematica
    z8 = 600; z9 = 150; z7 = 100;
k = 5/3; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
t[a_] := Table[d[a, b], {b, a, z8}]
u[n_] := Delete[t[n], Position[t[n], 0]]
Table[u[n], {n, 1, 15}]
t = Table[u[n], {n, 1, z8}];
Flatten[Position[t, {}]]
u = Flatten[Delete[t, Position[t, {}]]];
x[n_] := u[[3 n - 2]];
Table[x[n], {n, 1, z7}]   (* A196088 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]  (* A196089 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]  (* A196090 *)
x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
f = Table[x1[n], {n, 1, z9}];
x2 = Delete[f, Position[f, 0]]  (* A196091 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]  (* A196092 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]  (* A196093 *)

A196105 Positive integers a for which there is a (7/4)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 26, 27, 28, 28, 29, 30, 31, 33, 34, 34, 35, 36, 36, 37, 38, 39, 40, 42, 42, 42, 43, 44, 44, 44, 45, 46, 47, 48, 50, 51, 52, 52, 52, 53, 54, 55, 56, 56, 57, 58, 60, 60, 60, 61, 62, 62, 63, 63, 64, 65, 66, 66
Offset: 1

Views

Author

Clark Kimberling, Sep 28 2011

Keywords

Comments

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

Crossrefs

Cf. A195770, A196106, A196107, A196108.

Programs

  • Mathematica
    z8 = 900; z9 = 250; z7 = 200;
k = 7/4; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
t[a_] := Table[d[a, b], {b, a, z8}]
u[n_] := Delete[t[n], Position[t[n], 0]]
Table[u[n], {n, 1, 15}]
t = Table[u[n], {n, 1, z8}];
Flatten[Position[t, {}]]
u = Flatten[Delete[t, Position[t, {}]]];
x[n_] := u[[3 n - 2]];
Table[x[n], {n, 1, z7}]  (* A196105 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]  (* A196106 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]  (* A196107 *)
x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
f = Table[x1[n], {n, 1, z9}];
x2 = Delete[f, Position[f, 0]]  (* A196108 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]  (* A196109 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]  (* A196110 *)

A196383 Positive integers a for which there is a (-5)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Oct 01 2011

Keywords

Comments

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

Crossrefs

Cf. A195770, A196384, A196385, A196386.

Programs

  • Mathematica
    z8 = 900; z9 = 250; z7 = 200;
pIntegerQ := IntegerQ[#1] && #1 > 0 &;
k = -5; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[pIntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
t[a_] := Table[d[a, b], {b, a, z8}]
u[n_] := Delete[t[n], Position[t[n], 0]]
Table[u[n], {n, 1, 15}]
t = Table[u[n], {n, 1, z8}];
Flatten[Position[t, {}]]
u = Flatten[Delete[t, Position[t, {}]]];
x[n_] := u[[3 n - 2]];
Table[x[n], {n, 1, z7}]  (* A196383 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]  (* A196384 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]  (* A196385 *)
x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
f = Table[x1[n], {n, 1, z9}];
x2 = Delete[f, Position[f, 0]]  (* A196386 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]  (* A196387 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]  (* A196388 *)

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

Original entry on oeis.org

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, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 22, 22, 22, 23, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 26
Offset: 1

Views

Author

Clark Kimberling, Sep 25 2011

Keywords

Comments

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

Examples

			(-1/2)-Pythagorean triples:
1,2,2
2,4,4
3,6,6
4,8,8
5,48,47
(For primitive triples, see A195875.)

Crossrefs

Cf. A195770, A195875.

Programs

  • Mathematica
    z8 = 800; z9 = 400; z7 = 100;
k = -1/2; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
t[a_] := Table[d[a, b], {b, a, z8}]
u[n_] := Delete[t[n], Position[t[n], 0]]
Table[u[n], {n, 1, 15}]
t = Table[u[n], {n, 1, z8}];
Flatten[Position[t, {}]]
u = Flatten[Delete[t, Position[t, {}]]];
x[n_] := u[[3 n - 2]];
Table[x[n], {n, 1, z7}]    (* A195872 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]    (* A195873 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]    (* A195874 *)
x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
f = Table[x1[n], {n, 1, z9}];
x2 = Delete[f, Position[f, 0]]    (* A195875 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]    (* A195876 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]    (* A195877 *)

A195879 Positive integers a for which there is a (1/2)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

2, 3, 4, 5, 6, 6, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23, 24, 24, 25, 25, 26, 26, 26, 26, 26, 27, 27, 28, 28, 28, 28, 29, 29, 30, 30, 30, 30, 31
Offset: 1

Views

Author

Clark Kimberling, Sep 25 2011

Keywords

Comments

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

Crossrefs

Cf. A195770, A195880, A195882.

Programs

  • Mathematica
    z8 = 800; z9 = 400; z7 = 100;
k = 1/2; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
t[a_] := Table[d[a, b], {b, a, z8}]
u[n_] := Delete[t[n], Position[t[n], 0]]
Table[u[n], {n, 1, 15}]
t = Table[u[n], {n, 1, z8}];
Flatten[Position[t, {}]]
u = Flatten[Delete[t, Position[t, {}]]];
x[n_] := u[[3 n - 2]];
Table[x[n], {n, 1, z7}]  (* A195879 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]  (* A195880 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]  (* A195881 *)
x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
f = Table[x1[n], {n, 1, z9}];
x2 = Delete[f, Position[f, 0]]  (* A195882 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]  (* A195883 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]  (* A195884 *)

A195918 Positive integers a for which there is a (-3/2)-Pythagorean triple (a,b,c) satisfying a<=b.

Original entry on oeis.org

2, 3, 4, 5, 6, 6, 7, 8, 9, 9, 10, 10, 10, 11, 12, 12, 13, 14, 14, 15, 15, 15, 15, 15, 16, 16, 17, 18, 18, 18, 18, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23, 24, 24, 25, 25, 26, 26, 26, 27, 27, 27, 28, 28, 29, 30, 30, 30, 30, 30, 30, 30, 30, 32, 32, 32, 32, 33, 33, 33, 34
Offset: 1

Views

Author

Clark Kimberling, Sep 26 2011

Keywords

Comments

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

Crossrefs

Cf. A195770, A195919, A195920, A195921.

Programs

  • Mathematica
    z8 = 800; z9 = 400; z7 = 100;
k = -3/2; c[a_, b_] := Sqrt[a^2 + b^2 + k*a*b];
d[a_, b_] := If[IntegerQ[c[a, b]], {a, b, c[a, b]}, 0]
t[a_] := Table[d[a, b], {b, a, z8}]
u[n_] := Delete[t[n], Position[t[n], 0]]
Table[u[n], {n, 1, 15}]
t = Table[u[n], {n, 1, z8}];
Flatten[Position[t, {}]]
u = Flatten[Delete[t, Position[t, {}]]];
x[n_] := u[[3 n - 2]];
Table[x[n], {n, 1, z7}]    (* A195918 *)
y[n_] := u[[3 n - 1]];
Table[y[n], {n, 1, z7}]    (* A195919 *)
z[n_] := u[[3 n]];
Table[z[n], {n, 1, z7}]    (* A195920 *)
x1[n_] := If[GCD[x[n], y[n], z[n]] == 1, x[n], 0]
y1[n_] := If[GCD[x[n], y[n], z[n]] == 1, y[n], 0]
z1[n_] := If[GCD[x[n], y[n], z[n]] == 1, z[n], 0]
f = Table[x1[n], {n, 1, z9}];
x2 = Delete[f, Position[f, 0]]    (* A195921 *)
g = Table[y1[n], {n, 1, z9}];
y2 = Delete[g, Position[g, 0]]    (* A195922 *)
h = Table[z1[n], {n, 1, z9}];
z2 = Delete[h, Position[h, 0]]    (* A195923 *)
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