%I #24 Oct 17 2019 22:54:42

%S 8,125,512,1000,2197,4913,5832,8000,15625,17576,24389,32768,39304,

%T 50653,64000,68921,91125,125000,140608,148877,195112,226981,274625,

%U 314432,373248,389017,405224,512000,551368,614125,704969,729000,912673,941192

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

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

%C In other words, a(n)=(A000404(n))^3. - _Artur Jasinski_, Nov 29 2007

%C 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

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

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

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

%t 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 *)

%t Select[Range[100]^3, Length[DeleteCases[PowersRepresentations[#, 2, 2], w_ /; MemberQ[w, 0]]] > 0 &] (* _Michael De Vlieger_, May 11 2016 *)

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

%K nonn

%O 1,1

%A _Patrick De Geest_, Sep 15 1999

%E Edited by _N. J. A. Sloane_, May 15 2008 at the suggestion of _R. J. Mathar_