A293649 Sum of two coprime positive cubes in at least 2 ways, but not the sum of 2 non-coprime positive cubes.

1729, 20683, 40033, 149389, 195841, 327763, 443889, 684019, 704977, 1845649, 2048391, 2418271, 2691451, 3242197, 3375001, 4342914, 4931101, 5318677, 5772403, 5799339, 6058747, 7620661, 8872487, 9443761, 10702783, 10765603, 13623913, 14916727

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

			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.
		

Links

• Rosalie Fay, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A023050 (3 ways); A272885 (cubefree with positive cubes).

Cf. A159843, A293648 (allows negatives).

Programs

Mathematica

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 *)