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

1,2

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Index to sequences related to sums of cubes

Example

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

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 *)

Crossrefs

Contained in A045980. Contains A024670.

Primes in this sequence: A002407.

Cf. A060464.

Sequence in context: A165480 A285468 A060258 * A347809 A048029 A048009

Adjacent sequences: A307582 A307583 A307584 * A307586 A307587 A307588

Keyword

nonn

Author

Robert Israel, Apr 15 2019

Status

approved