A383879 a(n) is the smallest integer k such that the Diophantine equation x^3 + y^3 + z^3 + w^3 = k^n, where 0 < x < y < z < w has exactly n integer solutions.

100, 42, 55, 34, 74

Offset

1,1

Comments

If it exists, a(6) > 200. - Sean A. Irvine, May 19 2025

Links

Table of n, a(n) for n=1..5.

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 exactly 3 solutions.

Mathematica

f[n_]:=Do[v=Select[PowersRepresentations[k^n, 4, 3], 0<#[[1]]<#[[2]]<#[[3]]<#[[4]]&]; d={n, k, v, Length@v}; If[d[[-1]]==n, Return[d]], {k, 100}]; Do[Print[f[n]], {n, 4}]

Crossrefs

Cf. A383689.

Sequence in context: A298574 A077489 A371993 * A153674 A008903 A033420

Adjacent sequences: A383876 A383877 A383878 * A383880 A383881 A383882

Keyword

nonn,hard,more

Author

Zhining Yang, May 13 2025

Status

approved