A050803 Cubes expressible as the sum of two nonzero squares in at least one way.

8, 125, 512, 1000, 2197, 4913, 5832, 8000, 15625, 17576, 24389, 32768, 39304, 50653, 64000, 68921, 91125, 125000, 140608, 148877, 195112, 226981, 274625, 314432, 373248, 389017, 405224, 512000, 551368, 614125, 704969, 729000, 912673, 941192

Offset: 1

Author

Patrick De Geest, Sep 15 1999

Keywords

• nonn

Comments

Root values equal terms from sequence A000404 'Sum of 2 nonzero squares'.

In other words, a(n)=(A000404(n))^3. - Artur Jasinski, Nov 29 2007

Obviously, if n and m are different members of this sequence, then n*m is also a member of this sequence. Additionally, if k^3 is a member of this sequence and k is not in A050804, then k^6 is also a member of this sequence. - Altug Alkan, May 11 2016

Examples

			551368 or 82^3 = 82^2 + 738^2 = 242^2 + 702^2.
		

References

• Ian Stewart, "Game, Set and Math", Chapter 8 'Close Encounters of the Fermat Kind', Penguin Books, Ed. 1991, pp. 107-124.

Links

• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000404, A050802, A050803, A135786, A135787, A135788.

Programs

Mathematica

a[n_]:=Module[{c=0},i=1; While[i^2Jayanta Basu, May 30 2013 *)
Select[Range[100]^3, Length[DeleteCases[PowersRepresentations[#, 2, 2], w_ /; MemberQ[w, 0]]] > 0 &] (* Michael De Vlieger, May 11 2016 *)

Extensions

Edited by N. J. A. Sloane, May 15 2008 at the suggestion of R. J. Mathar