This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A293649 #19 Jun 29 2023 15:21:56
%S A293649 1729,20683,40033,149389,195841,327763,443889,684019,704977,1845649,
%T A293649 2048391,2418271,2691451,3242197,3375001,4342914,4931101,5318677,
%U A293649 5772403,5799339,6058747,7620661,8872487,9443761,10702783,10765603,13623913,14916727
%N A293649 Sum of two coprime positive cubes in at least 2 ways, but not the sum of 2 non-coprime positive cubes.
%C A293649 Not every term is cubefree; some are sb^3 where s is in A159843 and b > 1.
%H A293649 Rosalie Fay, <a href="/A293649/b293649.txt">Table of n, a(n) for n = 1..100</a>
%e A293649 14916727 = 246^3 + 31^3 = 240^3 + 103^3 and 246 & 31 are coprime, as are 240 & 103, but it is not also the sum of cubes of 2 non-coprime positive integers, so 14916727 is in the sequence.
%t A293649 Module[{smax = 2*10^8 (* upper limit of terms *), m, f, s}, m = smax^(1/3) // Ceiling; f[_] = {}; Reap[Do[AppendTo[f[s = i^3 + j^3], {i, j}]; If[s <= smax && Length[f[s]] >= 2 && AllTrue[f[s], CoprimeQ @@ #&], Sow[s]], {i, 1, m}, {j, i, m}]][[2, 1]]] // Sort (* _Jean-François Alcover_, Jun 29 2023 *)
%Y A293649 Cf. A023050 (3 ways); A272885 (cubefree with positive cubes).
%Y A293649 Cf. A159843, A293648 (allows negatives).
%K A293649 nonn
%O A293649 1,1
%A A293649 _Rosalie Fay_, Oct 16 2017