$T(n) = \sqrt n\,T(\sqrt n) + n\log n$

Question

I tried to solve this recursion equation with master theory, and it's not working in this way.

How many arrays exist in each step in the recursion tree?

And how can I solve this problem with another way?

Answer 1

The direct way: consider the change of variable $$S(n)=\frac{T(n)}n-2\log n.$$