A290400 Primes p such that Diophantine equation x + y + z = p with x*y*z = k^3 (0 < x <= y <= z) has a unique solution.
3, 7, 13, 17, 19, 23, 29, 37, 53, 71, 101, 149, 157, 317, 347
Offset: 1
Examples
7 is in the sequence since, of the triples whose sum is 7, i.e., (1, 1, 5), (1, 2, 4), (1, 3, 3), and (2, 2, 3), only one (i.e., (1, 2, 4)), yields a cube as its product: 1 * 2 * 4 = 8 = 2^3. 31 is not here, since the corresponding equation has two solutions: (1, 5, 25) and (1, 12, 18).
Links
- Tianxin Cai and Deyi Chen, A new variant of the Hilbert-Waring problem, Math. Comp. 82 (2013), 2333-2341.