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

1,1

Links

Table of n, a(n) for n=1..15.

Tianxin Cai and Deyi Chen, A new variant of the Hilbert-Waring problem, Math. Comp. 82 (2013), 2333-2341.

Example

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).

Crossrefs

Cf. A000040, A000578, A233386.

Sequence in context: A065057 A363636 A100807 * A040999 A172240 A129901

Adjacent sequences: A290397 A290398 A290399 * A290401 A290402 A290403

Keyword

nonn,more

Author

XU Pingya, Jul 29 2017

Status

approved