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%I #18 Apr 18 2024 11:41:14
%S 1,2,3,5,6,7,8,9,10,12,13,14,15,16,17,19,20,21,22,23,24,26,27,28,29,
%T 31,33,34,35,36,38,39,40,41,42,43,45,46,47,48,49,50,52,53,54,55,57,58,
%U 59,60,61,62,64,65,66,68,69,71,72,73,75,76,77,78,79,80,83,84,85,86,87
%N Positive integers that are not the sum of exactly four positive cubes.
%C It is conjectured that this sequence is finite, with 7373170279850 as its last member. - _Charles R Greathouse IV_, Jan 14 2017
%H T. D. Noe, <a href="/A057905/b057905.txt">Table of n, a(n) for n = 1..1000</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. p. 5.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CubicNumber.html">Cubic Number</a>
%t pr[n_] := Select[ PowersRepresentations[n, 4, 3], FreeQ[#, 0] &]; Select[ Range[90], pr[#] == {} &] (* _Jean-François Alcover_, Nov 08 2012 *)
%o (PARI) list(lim)=my(v=List(),e=1+lim\1,x='x,t); t=sum(i=1,sqrtnint(e-4,3), x^i^3, O(x^e))^4; for(n=1,lim, if(polcoeff(t,n)==0, listput(v,n))); Vec(v) \\ _Charles R Greathouse IV_, Jan 14 2017
%Y Complement is A003327.
%K nonn
%O 1,2
%A _Eric W. Weisstein_
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