A096546 - OEIS

A096546

Values w associated with A096545(n), sorted on z, then on y and finally on x.

6, 9, 20, 19, 28, 25, 29, 41, 46, 46, 41, 44, 53, 58, 54, 67, 70, 69, 85, 72, 75, 90, 82, 71, 76, 81, 84, 87, 87, 87, 97, 88, 93, 88, 89, 90, 108, 96, 105, 110, 113, 116, 134, 139, 122, 103, 121, 108, 126, 111, 115, 120, 123, 127, 141, 132, 129, 160, 137, 159, 145, 171

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

For 0<x<y<z, the primitive quadruples (x,y,z,w) satisfy x^3 + y^3 + z^3 = w^3.

LINKS

David A. Corneth, Table of n, a(n) for n = 1..13798 (terms corresponding to z <= 8000)

Fred Richman, Sums of Three Cubes

EXAMPLE

Entry 87, for example, is associated with primitive quadruples (x, y, z, w)= (26, 55, 78, 87), (38, 48, 79, 87), (20, 54, 79, 87) satisfying x^3 + y^3 + z^3 = w^3, for 0<x<y<z=A096545(n), with n=28, 29, 30.

MATHEMATICA

s[w_] := Solve[0 < x < y < z && x^3 + y^3 + z^3 == w^3 && GCD[x, y, z, w] == 1, {x, y, z}, Integers];

xyzw = Reap[For[w = 1, w <= 200, w++, sw = s[w]; If[sw != {}, Print[{x, y, z, w} /. sw; Sow[{x, y, z, w} /. sw ]]]]][[2, 1]] // Flatten[#, 1]&;

SortBy[xyzw, {#[[3]]&, #[[2]]&, #[[1]]&}][[All, 4]] (* Jean-François Alcover, Mar 06 2020 *)

CROSSREFS

Primitive quadruples (x, y, z, w) = (A095868, A095867, A096545, A096546).

Sequence in context: A011988 A161782 A154783 * A376472 A357840 A355484

Adjacent sequences: A096543 A096544 A096545 * A096547 A096548 A096549

KEYWORD

nonn

AUTHOR

Lekraj Beedassy, Jun 25 2004

EXTENSIONS

Extended by Ray Chandler, Jun 28 2004

STATUS

approved