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

1,3

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

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 *)

Crossrefs

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

Sequence in context: A005455 A047338 A069811 * A326783 A326785 A327080

Adjacent sequences: A004823 A004824 A004825 * A004827 A004828 A004829

Keyword

nonn

Author

N. J. A. Sloane

Status

approved