A022555 Positive integers that are not the sum of two nonnegative cubes.

3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Omits the positive cubes (A000578) since m^3 = 0^3 + m^3, so is different from A057903.

Links

• T. D. Noe, Table of n, a(n) for n=1..10000
• Index entries for sequences related to sums of cubes

Crossrefs

Complement of A004999. Cf. A004825, A022561, A022566, A057903, A000578.

Programs

Maple

read transforms; cub := series(add(q^(n^3),n=0..100),q,1000001); t1 := series(cub^2,q,2000); t2 := POWERS(t1,q,2000); COMPl(t2);

Mathematica

r[n_] := Reduce[x >= 0 && y >= 0 && n == x^3 + y^3, {x, y}, Integers]; Select[ Range[80], r[#] === False &]  (* Jean-François Alcover, Nov 06 2012 *)
Select[Range@100,PowersRepresentations[#,2,3]=={}&] (* A much faster solution given by Giovanni Resta, Nov 06 2012 *)

Extensions

Edited by N. J. A. Sloane, Sep 28 2007