A332110 Numbers that are not the sum of ten (10) positive cubes.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 37, 39, 40, 41, 42, 44, 46, 47, 48, 49, 51, 53, 54, 55, 56, 58, 60, 61, 63, 65, 67, 68, 70, 72, 74, 75, 77, 79, 81, 82, 84, 86, 89, 91, 93, 96, 98, 100

Offset

1,2

Comments

The sequence is finite, with last term a(99) = 374.

Links

M. F. Hasler, Table of n, a(n) for n = 1..99 (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:
  10 = 10 * 1^3, 17 = 2^3 + 9 * 1^3, 24 = 2 * 2^3 + 8 * 1^3,
  31 = 3 * 2^3 + 7 * 1^3 and then 36 = 3^3 + 9 * 1^3.
The last 10 terms of the sequence are a(90 .. 99) = {196, 201, 208, 215, 222, 257, 294, 313, 320, 374}.

Mathematica

Select[Range[400], (pr = PowersRepresentations[#, 10, 3][[;; , 1]]) == {} || Max[pr] == 0 &] (* Amiram Eldar, Aug 24 2020 *)

Prog

(PARI) A332110=setminus([1..444], A003333_upto(555))

Crossrefs

Complement of A003333.

Cf. A332107, A332108, A332109, A332111 (analog for 7, 8, 9, resp. 11 cubes).

Sequence in context: A368365 A004746 A188301 * A178160 A052044 A253643

Adjacent sequences: A332107 A332108 A332109 * A332111 A332112 A332113

Keyword

nonn,fini,full

Author

M. F. Hasler, Aug 24 2020

Status

approved