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A290401
Smallest prime p such that the Diophantine equation x + y + z = p with x*y*z = k^3 (0 < x <= y <= z) has exactly n solutions.
0
3, 31, 47, 127, 137, 211, 271, 257, 397, 631, 661, 1039, 1879, 1471, 2203, 2707, 2179, 1321, 3169, 3319, 6247, 4507, 5569, 6871, 6481, 6121, 6271, 9521, 9421, 13441, 8677, 17029, 8539, 15349, 11971, 25171, 21139, 17851, 29761, 21031, 33769, 37591, 28429, 44987
OFFSET
1,1
LINKS
Tianxin Cai and Deyi Chen, A new variant of the Hilbert-Waring problem, Math. Comp. 82 (2013), 2333-2341.
EXAMPLE
a(3) = 47 because the corresponding equation has exactly three solutions: (2, 20, 25), (4, 16, 27) and (6, 9, 32), and there is no prime smaller than 47 for which this is the case.
CROSSREFS
KEYWORD
nonn
AUTHOR
XU Pingya, Jul 29 2017
EXTENSIONS
a(24) and a(28)-a(44) from Giovanni Resta, Jul 30 2017
STATUS
approved