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A332110
Numbers that are not the sum of ten (10) positive cubes.
5
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
KEYWORD
nonn,fini,full
AUTHOR
M. F. Hasler, Aug 24 2020
STATUS
approved