%N Numbers n such that n is not divisible by 5 and n^k is of the form a^2 + b^4 for all k not divisible by 4.
%C Numbers n such that n, n^2 and n^3 is in A111925 and n is not divisible by 5.
%C Since there cannot be fourth power in A111925, this sequence focuses on the values of k that is not divisible by 4 in definition.
%e 609076 is a term because 609076 = 710^2 + 18^4, 609076^2 = 581940^2 + 424^4, 609076^3 = 475342920^2 + 676^4 and it is not divisible by 5.
%o (PARI) isA111925(n) = for(b=1, sqrtnint(n-1, 4), if(issquare(n-b^4), return(1))); 0;
%o isok(n) = n%5 != 0 && isA111925(n) && isA111925(n^2) && isA111925(n^3);
%Y Cf. A111925.
%A _Altug Alkan_, Jun 12 2016