|
|
A004826
|
|
Numbers that are the sum of at most 4 positive cubes.
|
|
9
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|