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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

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 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-Fran├žois 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 November 17 08:17 EST 2018. Contains 317275 sequences. (Running on oeis4.)