13. Let $S_{n}=1+2+3+\cdots+n, n \in \mathbf{N}^{*}$. Find the maximum value of $f(n)=\frac{S_{n}}{(n+32) S_{n+1}}$.
$$
\begin{array}{l}
f(n)=\frac{S_{n}}{(n+32) S_{n+1}}=\frac{\frac{n(n+1)}{2}}{(n+32) \cdot \frac{(n+1)(n+2)}{2}}=\frac{n}{(n+2)(n+32)} \\
=\frac{n}{n^{2}+34 n+64}=\frac{1}{n+\frac{64}{n}+34} \leqslant \frac{1}{50} . \text{ The equality holds when } n=8 .
\end{array}
$$

Therefore, the maximum value of $f(n)=\frac{S_{n}}{(n+32) S_{n+1}}$ is $\frac{1}{50}$.