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A332111
Numbers that are not the sum of eleven (11) positive cubes.
4
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 38, 40, 41, 42, 43, 45, 47, 48, 49, 50, 52, 54, 55, 56, 57, 59, 61, 62, 64, 66, 68, 69, 71, 73, 75, 76, 78, 80, 82, 83, 85, 87, 90, 92, 94, 97, 99
OFFSET
1,2
COMMENTS
The sequence is finite, with last term a(92) = 321.
LINKS
M. F. Hasler, Table of n, a(n) for n = 1..92 (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:
11 = 11 * 1^3, 18 = 2^3 + 10 * 1^3, 25 = 2 * 2^3 + 9 * 1^3,
32 = 3 * 2^3 + 8 * 1^3 and then 37 = 3^3 + 10 * 1^3.
The last 23 terms of the sequence (not in the data section) are a(70 .. 92) = {101, 104, 106, 108, 111, 113, 118, 120, 125, 127, 132, 134, 139, 146, 153, 160, 171, 190, 197, 209, 216, 223, 321}.
MATHEMATICA
Select[Range[400], (pr = PowersRepresentations[#, 11, 3][[;; , 1]]) == {} || Max[pr] == 0 &] (* adapted from Amiram Eldar's code for A332110 *)
PROG
(PARI) A332111=setminus([1..333], A003333_upto(444))
CROSSREFS
Complement of A003334.
Cf. A332107, A332108, A332109, A332110 (analog for 7, 8, 9 and 10 cubes).
Sequence in context: A328869 A004744 A171987 * A072226 A247809 A247802
KEYWORD
nonn,fini,full
AUTHOR
M. F. Hasler, Aug 25 2020
STATUS
approved