

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
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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, SpringerVerlag, 2007, p. 379.


LINKS

Table of n, a(n) for n=1..68.
Index entries for sequences related to sums of cubes


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 precomputed 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 &] (* JeanFrançois 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



