Find $f(z)$ s.t $z=0$ is essential singular point for $f(z)$ but not an isolated singular point for $\frac{1}{f(z)}$

Question

the question is: give an example of a funciton $f(z)$ such that, $z=0$ is an Essential singular point for $f(z)$ and not an isolated singular point for $\frac{1}{f(z)}$

I thought about giving a function that has a sequence of singular points in the points $z=\frac{1}{n}$ but I have no idea how to formulate it. help\hints would be appreciated !