A353291 Integers whose cube is the sum of the cubes of four primes, not necessarily distinct.

12, 66, 336, 504, 588, 602, 756, 1092, 1248, 1470, 1638, 1848, 2142, 2184, 2289, 2394, 2772, 3094, 3192, 3276, 3885, 3948, 4242, 4284, 4368, 4410, 4578, 4620, 4788, 4830, 4998, 5166, 5460, 5544, 5586, 5670, 5754, 6006, 6216, 6552, 6636, 6708, 6804, 6930, 7014

Offset: 1

Author

Michel Marcus, Apr 09 2022

Keywords

• nonn

Examples

			12 is a term because 3^3 + 3^3 + 7^3 + 11^3 = 1728 = 12^3.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..53
• Zhichun Zhai, Problems related to Waring-Goldbach problem involving cubes of primes, arXiv:2201.07346 [math.GM], 2022. See Table 3 p. 4.

Crossrefs

Cube roots of the intersection of A346917 and A000578.

Programs

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);

Extensions

a(8) and beyond from Michael S. Branicky, Apr 09 2022