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

1,1

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.

Example

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

Prog

(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);

Crossrefs

Cube roots of the intersection of A346917 and A000578.

Sequence in context: A161805 A036399 A003200 * A200190 A270251 A165107

Adjacent sequences: A353288 A353289 A353290 * A353292 A353293 A353294

Keyword

nonn

Author

Michel Marcus, Apr 09 2022

Extensions

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

Status

approved