A384430 a(n) is the smallest positive integer k such that the Diophantine equation x^3 + y^3 + z^3 + w^3 = k^5, where 0 < x < y < z < w has exactly n integer solutions.

8, 9, 10, 13, 74, 23, 40, 88, 31, 22, 17, 56

Offset

1,1

Comments

a(13)>360.

Links

Table of n, a(n) for n=1..12.

Example

a(3)=10, because 10^5 = 6^3 + 24^3 + 34^3 + 36^3 = 12^3 + 16^3 + 34^3 + 38^3 = 10^3 + 20^3 + 30^3 + 40^3 and no integer less than 10 has 3 solutions.

Mathematica

s=Table[{k, Length@Select[PowersRepresentations[k^5, 4, 3], 0<#[[1]]<#[[2]]<#[[3]]<#[[4]]&]}, {k, 20}]; a=Table[SelectFirst[s, #[[2]]==k&], {k, 4}][[All, 1]]

Crossrefs

Cf. A383877, A384182.

Sequence in context: A067683 A338026 A359881 * A164276 A154967 A271211

Adjacent sequences: A384427 A384428 A384429 * A384431 A384432 A384433

Keyword

nonn,more

Author

Zhining Yang, Jun 14 2025

Status

approved