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A332109
Numbers that are not the sum of nine (9) positive cubes.
5
1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 36, 38, 39, 40, 41, 43, 45, 46, 47, 48, 50, 52, 53, 54, 55, 57, 59, 60, 62, 64, 66, 67, 69, 71, 73, 74, 76, 78, 80, 81, 83, 85, 88, 90, 92, 95, 97, 99, 102
OFFSET
1,2
COMMENTS
The sequence is finite, with last term a(114) = 471.
LINKS
M. F. Hasler, Table of n, a(n) for n = 1..114 (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:
9 = 9 * 1^3, 16 = 2^3 + 8 * 1^3, 23 = 2 * 2^3 + 7 * 1^3,
30 = 3 * 2^3 + 6 * 1^3 and then 35 = 3^3 + 8 * 1^3.
The last 10 terms of the sequence are a(105 .. 114) = {293, 305, 310, 312, 319, 347, 366, 373, 422, 471}.
MATHEMATICA
Select[Range[500], (pr = PowersRepresentations[#, 9, 3][[;; , 1]]) == {} || Max[pr] == 0 &] (* Amiram Eldar, Aug 24 2020 *)
PROG
(PARI) A332109=setminus([1..555], A003332_upto(666))
CROSSREFS
Complement of A003332.
Cf. A332107, A332108, A332110 (analog for 7, 8 and 10 cubes, respectively).
Sequence in context: A343107 A004745 A158037 * A287519 A307646 A246786
KEYWORD
nonn,fini,full
AUTHOR
M. F. Hasler, Aug 24 2020
STATUS
approved