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
a(1)=4 corresponding to the quadruple (3,4,5,6).
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, 2]] (* Jean-François Alcover, Mar 06 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ray Chandler, Jun 28 2004
STATUS
approved