Sums of proper divisors follow the Erdős--Kac law

Paul Pollack, Lee Troupe

Let $s(n)={\sum }_{d\mid n,d<n}d$ denote the sum of the proper divisors of $n$. The second-named author proved that $\omega (s(n))$ has normal order $\log \log n$, the analogue for $s$-va…