Efficient way of knowing large factors of $\phi(n)$ given small prime factors and $n$

Question

Knowing large prime factor$(r > n^{1/4})$ of $\phi(n)$ can easily factorize n and hence learn $\phi(n)$.

If we have knowledge on all small prime factors $(2< r_i << n^{1/4})$ of $\phi(n)$ then, is there any efficient way to factorize $n$ and $\phi(n)$?

Note: $n$ is an RSA number