A051347 Numbers that are the sum of two (possibly negative) cubes in at least 2 ways.

91, 152, 189, 217, 513, 721, 728, 999, 1027, 1216, 1512, 1729, 1736, 2457, 3087, 3367, 4104, 4706, 4921, 4977, 5103, 5256, 5768, 5824, 5859, 6832, 7657, 7992, 8216, 8587, 8911, 9728, 9919, 10621, 10712, 11375, 12096, 12663, 12691, 12824, 13832, 13851

Offset: 1

Author

Colin Mallows

Keywords

• nonn
• nice

Examples

			91 = 3^3 + 4^3 = (-5)^3 + 6^3; 152 = 3^3 + 5^3 = (-4)^3 + 6^3; 189 = 4^3 + 5^3 = (-3)^3 + 6^3; ...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A051383, A051384.

Programs

Mathematica

ok[n_] := If[Length[PowersRepresentations[n, 2, 3]] >= 2, True, r = Reduce[n == x^3 + y^3, {x, y}, Integers]; If[r === False, False, Length[Union[Sort /@ ({x, y} /. {ToRules[r]})]] >= 2]]; Select[Range[13860], If[ok[#], Print[#]; True, False] &] (* Jean-François Alcover, Apr 11 2011 *)

PARI

is(n)=#thue(thueinit(z^3+1),n)>=2 \\ Ralf Stephan, Oct 18 2013

Extensions

Extended by Ray Chandler, Jan 30 2009