  Let $\omega(n)$ (resp. $\Omega(n)$) denote the number of prime divisors
(resp. with multiplicity) of a natural number $n$. In 1917, Hardy and Ramanujan
proved that the normal order of $\omega(n)$ is $\log\log n$, and the same is
true of $\Omega(n)$; roughly speaking, a typical natural number $n$ has about
$\log\log n$ prime factors. We prove a similar result for $\omega(s(n))$, where
$s(n)$ denotes the sum of the proper divisors of $n$: For any $\epsilon > 0$
and all $n \leq x$ not belonging to a set of size $o(x)$, \[ |\omega(s(n)) -
\log\log s(n)| < \epsilon \log\log s(n) \] and the same is true for
$\Omega(s(n))$.
