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%I #11 Jun 24 2017 13:46:36
%S 1,91,3367,16776487,506433677359393
%N Smallest positive number that can be written in n ways as a sum of two (not necessarily positive) coprime cubes.
%D R. K. Guy, Unsolved Problems in Number Theory, Section D1.
%H D. J. Bernstein, <a href="http://pobox.com/~djb/papers/sortedsums.dvi">Enumerating solutions to p(a) + q(b) = r(c) + s(d)</a>
%t (* This naive program is not convenient for more than 4 terms *) max = 300; Clear[k]; k[_] = 0; t = Reap[ Do[ Do[z = x^3 + y^3; If[CoprimeQ[x, y], k[z] = k[z] + 1]; z = -x^3 + y^3; If[CoprimeQ[x, y], k[z] = k[z] + 1]; kz = k[z]; If[kz > 1, Sow[{z, kz}]], {y, x, max}], {x, 1, max}]][[2, 1]]; s = Sort[t]; a[n_] := Select[s, #[[2]] == n &, 1][[1, 1]]; a[1] = 1; Table[a[n], {n, 1, 4}] (* _Jean-François Alcover_, Jan 11 2013 *)
%Y Cf. A047696.
%K nonn,nice,hard
%O 1,2
%A _N. J. A. Sloane_
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