%I #18 Jul 17 2020 03:50:18
%S 6,9,20,19,28,25,29,41,46,46,41,44,53,58,54,67,70,69,85,72,75,90,82,
%T 71,76,81,84,87,87,87,97,88,93,88,89,90,108,96,105,110,113,116,134,
%U 139,122,103,121,108,126,111,115,120,123,127,141,132,129,160,137,159,145,171
%N Values w associated with A096545(n), sorted on z, then on y and finally on x.
%C For 0<x<y<z, the primitive quadruples (x,y,z,w) satisfy x^3 + y^3 + z^3 = w^3.
%H David A. Corneth, <a href="/A096546/b096546.txt">Table of n, a(n) for n = 1..13798</a> (terms corresponding to z <= 8000)
%H Fred Richman, <a href="http://math.fau.edu/Richman/cubes.htm">Sums of Three Cubes</a>
%e 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.
%t 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];
%t 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]&;
%t SortBy[xyzw, {#[[3]]&, #[[2]]&, #[[1]]&}][[All, 4]] (* _Jean-François Alcover_, Mar 06 2020 *)
%Y Primitive quadruples (x, y, z, w) = (A095868, A095867, A096545, A096546).
%K nonn
%O 1,1
%A _Lekraj Beedassy_, Jun 25 2004
%E Extended by _Ray Chandler_, Jun 28 2004