A332107 Numbers that are not the sum of seven (7) positive cubes.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 34, 36, 37, 38, 39, 41, 43, 44, 45, 46, 48, 50, 51, 52, 53, 55, 57, 58, 60, 62, 63, 64, 65, 67, 69, 71, 72, 74, 76, 78, 79, 81, 82, 83, 86, 88, 89, 90, 93, 95, 97, 100

Offset

1,2

Comments

The sequence is finite, with last term a(208) = 2408.

Links

M. F. Hasler, Table of n, a(n) for n = 1..208 (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 7 = 7 * 1^3, 14 = 2^3 + 6 * 1^3, 21 = 2 * 2^3 + 5 * 1^3, ...
The last 10 terms of the sequence are a(199 .. 208) = {1078, 1094, 1364, 1409, 1579, 1582, 1796, 2030, 2382, 2408}.

Mathematica

Select[Range[100], (pr = PowersRepresentations[#, 7, 3][[;; , 1]]) == {} || Max[pr] == 0 &] (* Amiram Eldar, Aug 24 2020 *)

Prog

(PARI) A332107=setminus([1..2440], A003330_upto(2444))

Crossrefs

Complement of A003330.

Cf. A332108, A332109, A332110, A332111: analog for eight, ..., eleven cubes.

Sequence in context: A195178 A043092 A023801 * A267305 A302478 A356939

Adjacent sequences: A332104 A332105 A332106 * A332108 A332109 A332110

Keyword

nonn,fini,full

Author

M. F. Hasler, Aug 24 2020

Status

approved