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 A386521 #19 Aug 16 2025 22:46:03
%S A386521 1,3,4,5,6,10,13,22,27,34,36,42,43,47,62,72,76,87,95,102,111,183,251,
%T A386521 279,315,322,327,344,483,490,528,615,708,762,1170,1302,2295,2526,3282,
%U A386521 3382,6012
%N A386521 Integers w such that the Diophantine equation x^2 + y^3 + z^4 = w^5 with GCD(x,y,z)=1 has no positive integer solutions.
%C A386521 a(42) > 6500. - _Giovanni Resta_, Aug 12 2025
%e A386521 9 is not a term because 9^5 = x^2 + y^3 + z^4 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 A386521 f[w_]:=(c=0;zz=w^5;Do[yy=zz-z^4;Do[xx=yy-y^3;x=Sqrt@xx;
%t A386521 If[IntegerQ@x,If[GCD[x,y,z]==1,c++]],{y,Floor[yy^(1/3)]}],{z,Floor[zz^(1/4)]}];c);Select[Range@50,f@#==0&]
%Y A386521 Cf. A386373, A386377.
%K A386521 nonn,more
%O A386521 1,2
%A A386521 _David A. Corneth_ and _Zhining Yang_, Jul 24 2025
%E A386521 a(41) from _Giovanni Resta_, Aug 12 2025