cp's OEIS Frontend

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.

%I A384182 #18 Jul 21 2025 13:13:20
%S A384182 6,9,15,34,20,19,66,28,36,35,26,30,355,97,44,329,151,65,590,89,48,42,
%T A384182 129,54,70,99,56,178,580,128,110,392,107,518,63,125,90,887,242,78,100,
%U A384182 138,105,96,235,141,281,205,326,1094,117,108,197,860,159,174,291,134
%N 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.
%C A384182 a(131)>1600.
%H A384182 Zhining Yang, <a href="/A384182/b384182.txt">Table of n, a(n) for n = 1..130</a>
%e A384182 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.
%t A384182 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]]
%Y A384182 Cf. A383877.
%K A384182 nonn
%O A384182 1,1
%A A384182 _Zhining Yang_, May 21 2025