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A159843
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Sums of two rational cubes.
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9
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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
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1,2
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COMMENTS
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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
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REFERENCES
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H. Cohen, Number Theory. I, Tools and Diophantine Equations, Springer-Verlag, 2007, p. 379.
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LINKS
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Table of n, a(n) for n=1..68.
Index entries for sequences related to sums of cubes
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FORMULA
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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
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MATHEMATICA
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(* 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 *)
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CROSSREFS
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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
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KEYWORD
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nice,nonn
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AUTHOR
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Steven Finch, Apr 23 2009
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STATUS
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approved
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