

A020897


Sum of two nonzero rational cubes.


7



2, 6, 7, 9, 12, 13, 15, 16, 17, 19, 20, 22, 26, 28, 30, 31, 33, 34, 35, 37, 42, 43, 48, 49, 50, 51, 53, 54, 56, 58, 61, 62, 63, 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, 120
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OFFSET

1,1


COMMENTS

n such that x^3 + y^3 = n*z^3 has a solution in nonnegative integers x,y,z.


LINKS

Table of n, a(n) for n=1..65.
Steven R. Finch, On a Generalized FermatWiles Equation [broken link]
Steven R. Finch, On a Generalized FermatWiles Equation [From the Wayback Machine]


MATHEMATICA

(* A naive program with a few precomputed terms *) nmax = 120; xmax = 2000; CubeFreePart[n_] := Times @@ Power @@@ ({#[[1]], Mod[#[[2]], 3]} & /@ FactorInteger[n]); nn = Reap[Do[n = CubeFreePart[x*y*(x+y)]; If[1 < n <= nmax, Sow[n]], {x, 1, xmax}, {y, x, xmax}]][[2, 1]] // Union; A020897 = 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 02 2012 *)


CROSSREFS

Sequence in context: A190784 A061416 A190247 * A020898 A184779 A200926
Adjacent sequences: A020894 A020895 A020896 * A020898 A020899 A020900


KEYWORD

nonn,nice


AUTHOR

Steven Finch


EXTENSIONS

Offset corrected by Arkadiusz Wesolowski, Aug 15 2013


STATUS

approved



