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

1,1

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

References

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

Links

Table of n, a(n) for n=1..34.

Index entries for sequences related to sums of squares

Example

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

Mathematica

a[n_]:=Module[{c=0}, i=1; While[i^2<n && c!=1, If[IntegerQ[Sqrt[n-i^2]], c=1]; i++]; c]; Select[Range[98]^3, a[#]==1&] (* Jayanta Basu, May 30 2013 *)
Select[Range[100]^3, Length[DeleteCases[PowersRepresentations[#, 2, 2], w_ /; MemberQ[w, 0]]] > 0 &] (* Michael De Vlieger, May 11 2016 *)

Crossrefs

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

Sequence in context: A231638 A065082 A053058 * A016791 A061103 A264143

Adjacent sequences: A050800 A050801 A050802 * A050804 A050805 A050806

Keyword

nonn

Author

Patrick De Geest, Sep 15 1999

Extensions

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

Status

approved