A293646 Sum of two (possibly negative) coprime cubes, but not the sum of 2 non-coprime cubes.

1, 2, 7, 9, 19, 26, 28, 35, 37, 61, 63, 65, 91, 98, 117, 124, 126, 127, 133, 169, 215, 217, 218, 271, 279, 316, 331, 335, 341, 342, 344, 351, 370, 386, 387, 397, 407, 468, 469, 485, 511, 539, 547, 559, 602, 604, 631, 637, 657, 665, 721, 730, 737, 793, 817, 819

Offset

1,2

Comments

Not every term is cubefree; some are sb^3 where s is in A159843 and b > 1.

Links

Rosalie Fay, Table of n, a(n) for n = 1..101 (corrected by Ray Chandler, Jan 19 2019)

Example

344 = 7^3 + 1^3 and 344 is not also the sum of cubes of 2 non-coprime integers, so 344 is in the sequence.
152 = 6^3 + (-4)^3 and 6 and -4 are not coprime, so 152 is not in the sequence.

Mathematica

s[n_] := CoprimeQ @@@ ({x, y} /. Solve[n == x^3 + y^3, {x, y}, Integers]);
Reap[For[k = 1, k < 2000, k++, If[Union[s[k]] == {True}, Print[k]; Sow[k]]]][[2, 1]] (* Jean-François Alcover, Feb 02 2023 *)

Crossrefs

Cf. A020895 (cubefree); A293645 (allows non-coprime); A293648, A293651

Sequence in context: A336770 A361706 A293645 * A020895 A174247 A343963

Adjacent sequences: A293643 A293644 A293645 * A293647 A293648 A293649

Keyword

nonn

Author

Rosalie Fay, Oct 16 2017

Status

approved