A047697 Smallest positive number that can be written in n ways as a sum of two (not necessarily positive) coprime cubes.

1, 91, 3367, 16776487, 506433677359393

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• hard

References

• R. K. Guy, Unsolved Problems in Number Theory, Section D1.

Links

• D. J. Bernstein, Enumerating solutions to p(a) + q(b) = r(c) + s(d)

Crossrefs

Cf. A047696.

Programs

Mathematica

(* 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 *)