A377444 a(n) is the smallest integer k such that the Diophantine equation x^3 + y^3 + z^3 = k^3, where 0 < x <= y <= z has exactly n integer solutions.

6, 18, 54, 87, 108, 216, 174, 348, 396, 324, 696, 864, 492, 1080, 984, 1728, 1584, 1296, 2160, 1440, 3312, 3132, 2880, 2592, 4176, 4230, 6624, 3960, 5184, 6264, 4320, 5760, 6480, 7200, 10200, 7920, 9936, 5940, 8640, 12060, 11520, 9900, 14256, 14400, 16560, 14760, 15660, 22140

Offset

1,1

Comments

All the terms seem to be multiple of 3.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..120 (terms 1..66 from Zhining Yang)

Example

a(2)=18, because 18^3 = 9^3 + 12^3 + 15^3 = 2^3 + 12^3 + 16^3 and no integer less than 18 has 2 solutions.

Mathematica

a = Table[SelectFirst[Table[{k, Length@Select[PowersRepresentations[k^3, 3, 3], #[[1]] > 0 &]}, {k, 3, 500, 3}], #[[2]] == k &], {k, 10}]

Prog

(Python)
from itertools import count
from sympy.solvers.diophantine.diophantine import power_representation
def A377444(n): return next(filter(lambda k:len(list(power_representation(k**3, 3, 3)))==n, count(1))) # Chai Wah Wu, Nov 19 2024

Crossrefs

Cf. A316359.

Sequence in context: A079843 A290582 A346071 * A076941 A357198 A006779

Adjacent sequences: A377441 A377442 A377443 * A377445 A377446 A377447

Keyword

nonn,easy

Author

Zhining Yang, Oct 28 2024

Status

approved