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 A159843 Sums of two rational cubes. 13
 1, 2, 6, 7, 8, 9, 12, 13, 15, 16, 17, 19, 20, 22, 26, 27, 28, 30, 31, 33, 34, 35, 37, 42, 43, 48, 49, 50, 51, 53, 54, 56, 58, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 75, 78, 79, 84, 85, 86, 87, 89, 90, 91, 92, 94, 96, 97, 98, 103, 104, 105, 106, 107, 110, 114, 115, 117 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjectured asymptotic (based on the random matrix theory) is given in Cohen (2007) on p. 378. The prime elements are listed in A166246. - Max Alekseyev, Oct 10 2009 REFERENCES H. Cohen, Number Theory. I, Tools and Diophantine Equations, Springer-Verlag, 2007, p. 379. LINKS FORMULA A cubefree integer c>2 is in this sequence iff the elliptic curve y^2=x^3+16*c^2 has positive rank. - Max Alekseyev, Oct 10 2009 MATHEMATICA (* A naive program with a few pre-computed terms *) nmax = 117; xmax = 2000; CubeFreePart[n_] := Times @@ Power @@@ ({#[[1]], Mod[#[[2]], 3]} & /@ FactorInteger[n]); nn = Join[{1}, Reap[ Do[n = CubeFreePart[x*y*(x + y)]; If[1 < n <= nmax, Sow[n]], {x, 1, xmax}, {y, x, xmax}]][[2, 1]] // Union]; A159843 = Select[ Union[nn, nn*2^3, nn*3^3, nn*4^3, {17, 31, 53, 67, 71, 79, 89, 94, 97, 103, 107}], # <= nmax &] (* Jean-François Alcover, Apr 03 2012 *) CROSSREFS Cf. A020894, A020895, A020897, A020898. Complement of A185345. Sequence in context: A047555 A184939 A043050 * A243652 A080780 A138168 Adjacent sequences:  A159840 A159841 A159842 * A159844 A159845 A159846 KEYWORD nice,nonn AUTHOR Steven Finch, Apr 23 2009 STATUS approved

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Last modified January 17 07:58 EST 2021. Contains 340214 sequences. (Running on oeis4.)