This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A387023 #10 Aug 21 2025 17:50:28
%S A387023 9,45,70,80,120,124,125,128,133,143,170,175,180,195,201,220,224,236,
%T A387023 252,264,275,278,296,308,311,312,330,332,336,337,352,354,355,360,362,
%U A387023 366,374,375,380,386,390,394,399,404,411,416,418,428,430,444,461,466,477,484,488,500
%N A387023 Integers w such that the Diophantine equation x^2 + y^3 + z^4 = w^5 where GCD(x,y,z)=1 has exactly 5 positive integer solutions.
%H A387023 Zhining Yang, <a href="/A387023/b387023.txt">Table of n, a(n) for n = 1..328</a>
%e A387023 444 is in the sequence because 444^5 = x^2 + y^3 + z^4 where GCD (x, y, z) = 1 has exactly 5 positive integer solutions: {676786, 25603, 343}, {342332, 25775, 345}, {4123199, 5503, 544}, {2451712, 21919, 919}, {3889117, 679, 1208}.
%t A387023 Do[w5=w^5;s={};c=0;
%t A387023 Do[yy=w5-z^4;Do[xx=yy-y^3;x=Sqrt@xx;
%t A387023 If[IntegerQ@x,If[GCD[x,y,z]==1,c++;AppendTo[s,{x,y,z}]]],{y,Floor[yy^(1/3)]}],{z,Floor[w5^(1/4)]}];
%t A387023 If[c==5,Print[w,s]],{w,100}]
%Y A387023 Cf. A386373, A386377, A386521.
%K A387023 nonn,new
%O A387023 1,1
%A A387023 _Zhining Yang_, Aug 13 2025