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

1,2

Comments

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

Example

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}.

Mathematica

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

Prog

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

Crossrefs

Complement of A003331.

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

Sequence in context: A154799 A020660 A047306 * A316228 A353935 A348782

Adjacent sequences: A332105 A332106 A332107 * A332109 A332110 A332111

Keyword

nonn,fini,full

Author

M. F. Hasler, Aug 24 2020

Status

approved