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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.
0
3, 7, 13, 17, 19, 23, 29, 37, 53, 71, 101, 149, 157, 317, 347
OFFSET
1,1
LINKS
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
KEYWORD
nonn,more
AUTHOR
XU Pingya, Jul 29 2017
STATUS
approved