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%I #26 Apr 18 2024 13:48:28
%S 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,
%T 30,31,32,34,36,37,38,39,41,43,44,45,46,48,50,51,52,53,55,57,58,60,62,
%U 63,64,65,67,69,71,72,74,76,78,79,81,82,83,86,88,89,90,93,95,97,100
%N Numbers that are not the sum of seven (7) positive cubes.
%C The sequence is finite, with last term a(208) = 2408.
%H M. F. Hasler, <a href="/A332107/b332107.txt">Table of n, a(n) for n = 1..208</a> (full sequence).
%H Brennan Benfield and Oliver Lippard, <a href="https://arxiv.org/abs/2404.08193">Integers that are not the sum of positive powers</a>, arXiv:2404.08193 [math.NT], 2024. See p. 4.
%e 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, ...
%e The last 10 terms of the sequence are a(199 .. 208) = {1078, 1094, 1364, 1409, 1579, 1582, 1796, 2030, 2382, 2408}.
%t Select[Range[100], (pr = PowersRepresentations[#, 7, 3][[;; , 1]]) == {} || Max[pr] == 0 &] (* _Amiram Eldar_, Aug 24 2020 *)
%o (PARI) A332107=setminus([1..2440],A003330_upto(2444))
%Y Complement of A003330.
%Y Cf. A332108, A332109, A332110, A332111: analog for eight, ..., eleven cubes.
%K nonn,fini,full
%O 1,2
%A _M. F. Hasler_, Aug 24 2020
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