A384182 a(n) is the smallest integer k such that the Diophantine equation x^3 + y^3 + z^3 + w^3 = k^4, where 0 < x < y < z < w has exactly n integer solutions.

6, 9, 15, 34, 20, 19, 66, 28, 36, 35, 26, 30, 355, 97, 44, 329, 151, 65, 590, 89, 48, 42, 129, 54, 70, 99, 56, 178, 580, 128, 110, 392, 107, 518, 63, 125, 90, 887, 242, 78, 100, 138, 105, 96, 235, 141, 281, 205, 326, 1094, 117, 108, 197, 860, 159, 174, 291, 134

Offset: 1

Author

Zhining Yang, May 21 2025

Keywords

• nonn

Comments

a(131)>1600.

Examples

			a(3)=15, because 15^4 = 13^3 + 21^3 + 23^3 + 30^3 = 11^3 + 16^3 + 21^3 + 33^3 = 9^3 + 11^3 + 21^3 + 34^3 and no integer less than 15 has 3 solutions.
		

Links

• Zhining Yang, Table of n, a(n) for n = 1..130

Crossrefs

Cf. A383877.

Programs

Mathematica

s=Table[{k, Length@Select[PowersRepresentations[k^4, 4, 3], 0<#[[1]]<#[[2]]<#[[3]]<#[[4]]&]}, {k, 50}];a=Table[SelectFirst[s, #[[2]]==k&], {k, 6}][[All, 1]]