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

Author

Rosalie Fay, Oct 16 2017

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)