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A293646
Sum of two (possibly negative) coprime cubes, but not the sum of 2 non-coprime cubes.
4
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
KEYWORD
nonn
AUTHOR
Rosalie Fay, Oct 16 2017
STATUS
approved