A332108 - OEIS

%I #20 Apr 18 2024 13:48:52

%S 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,

%T 30,31,32,33,35,37,38,39,40,42,44,45,46,47,49,51,52,53,54,56,58,59,61,

%U 63,65,66,68,70,72,73,75,77,79,80,82,84,87,89,90,91,94,96,98

%N Numbers that are not the sum of eight (8) positive cubes.

%C The sequence is finite, with last term a(142) = 620.

%H M. F. Hasler, <a href="/A332108/b332108.txt">Table of n, a(n) for n = 1..142</a>

%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:

%e   8 = 8 * 1^3, 15 = 2^3 + 7 * 1^3, 22 = 2 * 2^3 + 6 * 1^3,

%e   29 = 3 * 2^3 + 5 * 1^3 and then 34 = 3^3 + 7 * 1^3.

%e The last 10 terms of the sequence are a(133 .. 142) = {372, 381, 395, 407, 414, 421, 444, 463, 470, 620}.

%t Select[Range[650], (pr = PowersRepresentations[#, 8, 3][[;; , 1]]) == {} || Max[pr] == 0 &] (* _Amiram Eldar_, Aug 25 2020 * )

%o (PARI) A332108=setminus([1..620],A003331_upto(620))

%Y Complement of A003331.

%Y Cf. A332107, A332109, A332110 (analog for 7, 9 resp. 10 cubes).

%K nonn,fini,full

%O 1,2

%A _M. F. Hasler_, Aug 24 2020