A332108 Numbers that are not the sum of eight (8) positive cubes.

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 35, 37, 38, 39, 40, 42, 44, 45, 46, 47, 49, 51, 52, 53, 54, 56, 58, 59, 61, 63, 65, 66, 68, 70, 72, 73, 75, 77, 79, 80, 82, 84, 87, 89, 90, 91, 94, 96, 98

Offset: 1

Author

M. F. Hasler, Aug 24 2020

Keywords

• nonn
• fini
• full

Comments

The sequence is finite, with last term a(142) = 620.

Examples

			The smallest positive numbers not in the sequence are:
  8 = 8 * 1^3, 15 = 2^3 + 7 * 1^3, 22 = 2 * 2^3 + 6 * 1^3,
  29 = 3 * 2^3 + 5 * 1^3 and then 34 = 3^3 + 7 * 1^3.
The last 10 terms of the sequence are a(133 .. 142) = {372, 381, 395, 407, 414, 421, 444, 463, 470, 620}.
		

Links

• M. F. Hasler, Table of n, a(n) for n = 1..142
• Brennan Benfield and Oliver Lippard, Integers that are not the sum of positive powers, arXiv:2404.08193 [math.NT], 2024. See p. 4.

Crossrefs

Complement of A003331.

Cf. A332107, A332109, A332110 (analog for 7, 9 resp. 10 cubes).

Programs

Mathematica

Select[Range[650], (pr = PowersRepresentations[#, 8, 3][[;; , 1]]) == {} || Max[pr] == 0 &] (* Amiram Eldar, Aug 25 2020 *)

PARI

A332108=setminus([1..620],A003331_upto(620))