A004826 Numbers that are the sum of at most 4 positive cubes.

0, 1, 2, 3, 4, 8, 9, 10, 11, 16, 17, 18, 24, 25, 27, 28, 29, 30, 32, 35, 36, 37, 43, 44, 51, 54, 55, 56, 62, 63, 64, 65, 66, 67, 70, 72, 73, 74, 80, 81, 82, 88, 89, 91, 92, 93, 99, 100, 107, 108, 118, 119, 125, 126, 127, 128, 129, 130, 133, 134, 135

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Stated in Lee, p. 1: It is now known that when N is sufficiently large, the number of positive integers at most N that fail to be written in such a way (A022566) is slightly smaller than N^(37/42). Since any integer congruent to 4 (mod 9) is never a sum of three cubes, the number of summands here cannot in general be reduced. But of those four cubes, two of which (minicubes) need be at most N^theta, as long as theta >= 192/869. An asymptotic formula for the number of such representations is established when 1/4 < theta < 1/3. - Jonathan Vos Post, Jun 29 2010

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Siu-lun Alan Lee, On Waring's Problem: Two Cubes and Two Minicubes, arXiv:1006.5142 [math.NT], 2010.
• G. Villemin's Almanach of Numbers, Sum of Four Cubes (0 through 100).
• Index entries for sequences related to sums of cubes

Crossrefs

Cf. A022566 (Numbers that are not the sum of 4 nonnegative cubes). - Jonathan Vos Post, Jun 29 2010

Programs

Mathematica

Reap[For[k = 0, k <= 200, k++, If[PowersRepresentations[k, 4, 3] != {}, Print[k]; Sow[k]]]][[2, 1]] (* Jean-François Alcover, Oct 05 2018 *)