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

Author

Zhining Yang, Oct 28 2024

Keywords

• nonn
• easy

Comments

All the terms seem to be multiple of 3.

Examples

			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.
		

Links

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

Crossrefs

Cf. A316359.

Programs

Mathematica

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

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