|
%I #29 Oct 02 2023 20:52:53
%S 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,
%T 54,55,56,62,63,64,65,66,67,70,72,73,74,80,81,82,88,89,91,92,93,99,
%U 100,107,108,118,119,125,126,127,128,129,130,133,134,135
%N Numbers that are the sum of at most 4 positive cubes.
%C 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
%H T. D. Noe, <a href="/A004826/b004826.txt">Table of n, a(n) for n = 1..1000</a>
%H Siu-lun Alan Lee, <a href="http://arxiv.org/abs/1006.5142">On Waring's Problem: Two Cubes and Two Minicubes</a>, arXiv:1006.5142 [math.NT], 2010.
%H G. Villemin's Almanach of Numbers, <a href="http://villemin.gerard.free.fr/Wwwgvmm/Addition/NoSoCu4f.htm#Entier">Sum of Four Cubes (0 through 100)</a>.
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%t Reap[For[k = 0, k <= 200, k++, If[PowersRepresentations[k, 4, 3] != {}, Print[k]; Sow[k]]]][[2, 1]] (* _Jean-François Alcover_, Oct 05 2018 *)
%Y Cf. A022566 (Numbers that are not the sum of 4 nonnegative cubes). - _Jonathan Vos Post_, Jun 29 2010
%K nonn
%O 1,3
%A _N. J. A. Sloane_
|
