Voozh

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

(list; graph; refs; listen; history; text; internal format)

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

URL: https://oeis.org/A384430

⇱ A384430 - OEIS