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

1,2

Comments

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

Example

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}.

Mathematica

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

Prog

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

Crossrefs

Complement of A003332.

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

Sequence in context: A343107 A004745 A158037 * A287519 A307646 A246786

Adjacent sequences: A332106 A332107 A332108 * A332110 A332111 A332112

Keyword

nonn,fini,full,changed

Author

M. F. Hasler, Aug 24 2020

Status

approved