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%I #17 Apr 10 2022 14:13:38
%S 12,66,336,504,588,602,756,1092,1248,1470,1638,1848,2142,2184,2289,
%T 2394,2772,3094,3192,3276,3885,3948,4242,4284,4368,4410,4578,4620,
%U 4788,4830,4998,5166,5460,5544,5586,5670,5754,6006,6216,6552,6636,6708,6804,6930,7014
%N Integers whose cube is the sum of the cubes of four primes, not necessarily distinct.
%H Michael S. Branicky, <a href="/A353291/b353291.txt">Table of n, a(n) for n = 1..53</a>
%H Zhichun Zhai, <a href="https://arxiv.org/abs/2201.07346">Problems related to Waring-Goldbach problem involving cubes of primes</a>, arXiv:2201.07346 [math.GM], 2022. See Table 3 p. 4.
%e 12 is a term because 3^3 + 3^3 + 7^3 + 11^3 = 1728 = 12^3.
%o (PARI) list(lim)=my(v=List(), P=apply(p->p^3, primes(sqrtnint(lim\=1, 3)))); foreach(P, p, foreach(P, q, foreach(P, r, my(s=p+q+r, t); for(i=1, #P, t=s+P[i]; if(t>lim, break); if (ispower(t, 3, &rr), listput(v, rr)))))); v = Set(v);
%Y Cube roots of the intersection of A346917 and A000578.
%K nonn
%O 1,1
%A _Michel Marcus_, Apr 09 2022
%E a(8) and beyond from _Michael S. Branicky_, Apr 09 2022
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