State a function f(n) that is $O(n^3)$ and $\Omega(n)$ but is not in $\Theta(n^d)$ for any $ 1 \leq d\leq 3$

Question

State a function f(n) that is $O(n^3)$ and $\Omega(n)$ but is not in $\Theta(n^d)$ for any $ 1 \leq d\leq 3$

So far I don't think it's possible. But I could be wrong, any help would be appreciated.

Answer 1

Hint: think about logarithms.

Further hint: (hidden)

Consider $f(n)=n \log n$.