A383877 a(n) is the smallest integer k such that the Diophantine equation x^3 + y^3 + z^3 + w^3 = k^3, where 0 < x < y < z < w has exactly n integer solutions, or 0 if there is no such k.

14, 13, 55, 26, 52, 63, 70, 66, 56, 104, 102, 143, 161, 91, 117, 112, 78, 236, 180, 217, 198, 192, 140, 292, 216, 259, 156, 196, 344, 168, 210, 264, 325, 252, 406, 360, 380, 402, 315, 338, 234, 308, 351, 182, 396, 408, 399, 432, 441, 312, 474, 636, 513, 273, 336, 476, 618, 666

Offset

1,1

Comments

The largest term for k<=10000 is a(3569)=9828.

Conjecture: a(n) != 0 for all n.

Links

Zhining Yang, Table of n, a(n) for n = 1..1280

Example

a(3)=55, because 55^3 = 7^3 + 24^3 + 38^3 + 46^3 = 7^3 + 12^3 + 34^3 + 50^3 = 17^3 + 19^3 + 28^3 + 51^3 and no integer less than 55 has 3 solutions.

Mathematica

s=Table[{k, Length@Select[PowersRepresentations[k^3, 4, 3], 0<#[[1]]<#[[2]]<#[[3]]<#[[4]]&]}, {k, 100}];
a=Table[SelectFirst[s, #[[2]]==k&], {k, 9}][[All, 1]]

Crossrefs

Cf. A377444, A384439.

Sequence in context: A055125 A373160 A206564 * A076158 A174160 A199256

Adjacent sequences: A383874 A383875 A383876 * A383878 A383879 A383880

Keyword

nonn

Author

Zhining Yang, May 13 2025

Status

approved