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 A386377 #20 Aug 15 2025 10:09:09
%S A386377 0,1,0,0,0,0,2,2,5,0,1,1,0,1,1,1,3,2,1,2,2,0,2,2,4,1,0,2,2,1,2,1,13,0,
%T A386377 2,0,1,3,1,1,4,0,0,7,5,3,0,2,10,1,1,2,7,2,1,1,8,1,2,1,7,0,4,3,8,4,4,1,
%U A386377 1,5,1,0,11,1,2,0,3,1,3,5,12,7,2,2,2,2,0,1,14,2,2,1
%N A386377 a(n) is the number of solutions to the equation x^2 + y^3 + z^4 = w^5 where GCD(x, y, z)=1.
%H A386377 Zhining Yang, <a href="/A386377/b386377.txt">Table of n, a(n) for n = 1..4500</a> (terms 1..856 from David A. Corneth)
%H A386377 David A. Corneth, <a href="/A386377/a386377.gp.txt">Tuples (x, y, z, w) that are solutions to the equation</a>.
%H A386377 David A. Corneth, <a href="/A386377/a386377_1.gp.txt">PARI program</a>
%e A386377 a(9) = 5 because x^2 + y^3 + z^4 = 9^5 where GCD(x,y,z)=1 has 5 positive integer solutions :{220,22,1},{64,38,3},{241,7,5},{9,38,8},{118,29,12}.
%t A386377 f[w_]:=(c=0;zz=w^5;Do[yy=zz-z^4;Do[xx=yy-y^3;x=Sqrt@xx;
%t A386377 If[IntegerQ@x,If[GCD[x,y,z]==1,c++]],{y,Floor[yy^(1/3)]}],{z,Floor[zz^(1/4)]}];c);Array[f@#&, 30]
%Y A386377 Cf. A386373, A386521.
%K A386377 nonn
%O A386377 1,7
%A A386377 _David A. Corneth_ and _Zhining Yang_, Jul 20 2025