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A332108
Numbers that are not the sum of eight (8) positive cubes.
5
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
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
KEYWORD
nonn,fini,full
AUTHOR
M. F. Hasler, Aug 24 2020
STATUS
approved