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%I #18 Jan 03 2016 15:31:58
%S 91,152,189,217,513,721,728,999,1027,1216,1512,1729,1736,2457,3087,
%T 3367,4104,4706,4921,4977,5103,5256,5768,5824,5859,6832,7657,7992,
%U 8216,8587,8911,9728,9919,10621,10712,11375,12096,12663,12691,12824,13832,13851
%N Numbers that are the sum of two (possibly negative) cubes in at least 2 ways.
%H Alois P. Heinz, <a href="/A051347/b051347.txt">Table of n, a(n) for n = 1..1000</a>
%e 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; ...
%t 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 *)
%o (PARI) is(n)=#thue(thueinit(z^3+1),n)>=2 \\ _Ralf Stephan_, Oct 18 2013
%Y Cf. A051383, A051384.
%K nonn,nice
%O 1,1
%A _Colin Mallows_
%E Extended by _Ray Chandler_, Jan 30 2009
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