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.

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

Table of n, a(n) for n=1..44.

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

Cf. A000040, A000230, A000578.

Sequence in context: A256473 A119739 A163579 * A341928 A238663 A141966

Adjacent sequences: A290398 A290399 A290400 * A290402 A290403 A290404

Keyword

nonn

Author

XU Pingya, Jul 29 2017

Extensions

a(24) and a(28)-a(44) from Giovanni Resta, Jul 30 2017

Status

approved