2. Let $n$ be a natural number that is equal to the sum of its divisors that are less than $n$. For example, the number 28. What is the sum of the reciprocals of all its divisors?
III/2. Let $d_{1}, d_{2}, \ldots, d_{k}$ be the divisors of the number $n$ and let $1=d_{1}<d_{2}<\ldots<d_{k}=n$. Then $d_{i} \cdot d_{k+1-i}=n$, so $\frac{1}{d_{1}}+\frac{1}{d_{2}}+\ldots+\frac{1}{d_{k}}=\frac{d_{k}}{n}+\frac{d_{k-1}}{n}+\ldots+\frac{d_{1}}{n}=\frac{d_{k}+\left(d_{k-1}+\ldots+d_{1}\right)}{n}=$ $\frac{n+n}{n}=2$.