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

1,1

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..100

Example

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.

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 *)

Crossrefs

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

Cf. A159843, A293648 (allows negatives).

Sequence in context: A379656 A339818 A379849 * A272885 A272935 A284671

Adjacent sequences: A293646 A293647 A293648 * A293650 A293651 A293652

Keyword

nonn

Author

Rosalie Fay, Oct 16 2017

Status

approved