A095868 - OEIS

%I #18 Jul 17 2020 03:49:36

%S 3,1,7,3,18,4,11,6,27,3,2,16,29,15,12,22,7,36,50,34,38,58,19,14,31,25,

%T 28,26,38,20,45,21,32,25,17,25,15,19,33,29,50,23,86,94,19,12,49,13,23,

%U 16,3,9,44,13,72,5,38,69,44,3,12,107,31,1,71,1,22,96,65,48,69,48,46,59

%N Values x 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="/A095868/b095868.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 a(1)=3 corresponding to the quadruple (3,4,5,6).

%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, 1]] (* _Jean-François Alcover_, Mar 06 2020 *)

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

%K nonn

%O 1,1

%A _Ray Chandler_, Jun 28 2004