A096545 Ordered z such that, for 0

5, 8, 17, 18, 21, 22, 27, 33, 37, 37, 40, 41, 44, 49, 53, 54, 57, 61, 64, 65, 66, 69, 69, 70, 72, 74, 75, 78, 79, 79, 79, 84, 85, 86, 86, 87, 89, 90, 92, 96, 97, 97, 97, 99, 101, 102, 102, 104, 105, 108, 114, 116, 118, 121, 122, 123, 124, 124, 128, 131, 136, 136, 137

Offset: 1

Author

Lekraj Beedassy, Jun 25 2004

Keywords

• nonn

Comments

For corresponding values w see A096546.

Examples

			21 and 22, for instance, are terms because we have: 18^3 + 19^3 + 21^3 = 28^3 and 4^3 + 17^3 + 22^3 = 25^3.
		

References

• Y. Perelman, Solutions to x^3 + y^3 + z^3 = u^3, Mathematics can be Fun, pp. 316-9 Mir Moscow 1985.

Links

• David A. Corneth, Table of n, a(n) for n = 1..13798 (terms corresponding to z <= 8000)
• Fred Richman, Sums of Three Cubes

Crossrefs

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

Programs

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]&;
Sort[xyzw[[All, 3]]] (* Jean-François Alcover, Mar 06 2020 *)

Extensions

Edited, corrected and extended by Ray Chandler, Jun 28 2004