A307585 Positive sums of two distinct cubes (of arbitrary sign).

1, 7, 8, 9, 19, 26, 27, 28, 35, 37, 56, 61, 63, 64, 65, 72, 91, 98, 117, 124, 125, 126, 127, 133, 152, 169, 189, 208, 215, 216, 217, 218, 224, 243, 271, 279, 280, 296, 316, 331, 335, 341, 342, 343, 344, 351, 370, 386, 387, 397, 407, 448, 468, 469, 485, 488, 504, 511, 512, 513, 520, 539, 547, 559

Offset: 1

Author

Robert Israel, Apr 15 2019

Keywords

• nonn

Comments

All terms == 0, 1, 2, 7 or 8 (mod 9).

Examples

			a(3) = 8 = 0^3 + 2^3.
a(4) = 9 = 1^3 + 2^3.
a(5) = 19 = (-2)^3 + 3^3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index to sequences related to sums of cubes

Crossrefs

Contained in A045980. Contains A024670.

Primes in this sequence: A002407.

Cf. A060464.

Programs

Maple

filter:= proc(n) local d, dp, r;
   for d in numtheory:-divisors(n) do
     dp:= n/d;
     r:= 12*dp - 3*d^2;
     if r > 0 and issqr(r) and (sqrt(r)/6 + d/2)::integer then return true fi
   od;
   false
end proc:
select(filter, [$0..1000]);

Mathematica

filterQ[n_] := Module[{d, dp, r}, Catch[Do[dp = n/d; r = 12 dp - 3 d^2; If[r > 0 && IntegerQ[Sqrt[r]] && IntegerQ[Sqrt[r]/6 + d/2], Throw[True]], {d, Divisors[n]}]; False]];
Select[Range[1000], filterQ] (* Jean-François Alcover, Oct 17 2020, after Maple *)