A332109 Numbers that are not the sum of nine (9) positive cubes.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 36, 38, 39, 40, 41, 43, 45, 46, 47, 48, 50, 52, 53, 54, 55, 57, 59, 60, 62, 64, 66, 67, 69, 71, 73, 74, 76, 78, 80, 81, 83, 85, 88, 90, 92, 95, 97, 99, 102

Offset: 1

Author

M. F. Hasler, Aug 24 2020

Keywords

• nonn
• fini
• full

Comments

The sequence is finite, with last term a(114) = 471.

Examples

			The smallest positive numbers not in the sequence are:
  9 = 9 * 1^3, 16 = 2^3 + 8 * 1^3, 23 = 2 * 2^3 + 7 * 1^3,
  30 = 3 * 2^3 + 6 * 1^3 and then 35 = 3^3 + 8 * 1^3.
The last 10 terms of the sequence are a(105 .. 114) = {293, 305, 310, 312, 319, 347, 366, 373, 422, 471}.
		

Links

• M. F. Hasler, Table of n, a(n) for n = 1..114 (full sequence).
• 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 A003332.

Cf. A332107, A332108, A332110 (analog for 7, 8 and 10 cubes, respectively).

Programs

Mathematica

Select[Range[500], (pr = PowersRepresentations[#, 9, 3][[;; , 1]]) == {} || Max[pr] == 0 &] (* Amiram Eldar, Aug 24 2020 *)

PARI

A332109=setminus([1..555],A003332_upto(666))