$f(n)$ - the largest prime number that divides n. Prove that $\sum_{n=2}^{\infty} \frac{1}{nf(n)}$ converges.

Question

Given this problem for series convergence: $f(n)$ - the largest prime number that divides n. Prove that $\sum_{n=2}^{\infty} \frac{1}{nf(n)}$ converges.. I know that $\frac{1}{n^x}$ converges for $x >1$, but I want to know more clear solution. Thank you in advance