When does superdiagonal matrix have a single Jordan block

Question

Let $A$ be the superdiagonal matrix given by $A=(a_{ij})$ where $a_{i,i+1}=r_i$ are nonzero entries and all the other entries are $0$. When is $A$ similar to a single Jordan block with eigenvalue $0$ in term of the entries?
I know that $A$ is nilpotent, so its only eigenvalue is $\lambda=0$.