t1={};
Do[Do[If[x^2+y^2+z^2+w^3==n, AppendTo[t1, n]&&Break[]], {x, 0, n^(1/2)}, {y, x, (n-x^2)^(1/2)}, {z, y, (n-x^2-y^2)^(1/2)}, {w, 0, (n-x^2-y^2-z^2)^(1/3)}], {n, 0, 5.7*10^5}];
t2={};
Do[If[FreeQ[t1, k]==True, AppendTo[t2, k]], {k, 0, 5.7*10^5}];
t2