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%I #21 Feb 02 2023 15:28:32
%S 1,2,7,9,19,26,28,35,37,61,63,65,91,98,117,124,126,127,133,169,215,
%T 217,218,271,279,316,331,335,341,342,344,351,370,386,387,397,407,468,
%U 469,485,511,539,547,559,602,604,631,637,657,665,721,730,737,793,817,819
%N Sum of two (possibly negative) coprime cubes, but not the sum of 2 non-coprime cubes.
%C Not every term is cubefree; some are sb^3 where s is in A159843 and b > 1.
%H Rosalie Fay, <a href="/A293646/b293646.txt">Table of n, a(n) for n = 1..101</a> (corrected by Ray Chandler, Jan 19 2019)
%e 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.
%e 152 = 6^3 + (-4)^3 and 6 and -4 are not coprime, so 152 is not in the sequence.
%t s[n_] := CoprimeQ @@@ ({x, y} /. Solve[n == x^3 + y^3, {x, y}, Integers]);
%t Reap[For[k = 1, k < 2000, k++, If[Union[s[k]] == {True}, Print[k]; Sow[k]]]][[2, 1]] (* _Jean-François Alcover_, Feb 02 2023 *)
%Y Cf. A020895 (cubefree); A293645 (allows non-coprime); A293648, A293651
%K nonn
%O 1,2
%A _Rosalie Fay_, Oct 16 2017
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