Question 100
For a natural number $n$ we define $\tau(n)$ as the number of natural numbers that divide $n$, and we define $\sigma(n)$ as the sum of these divisors. Find all natural numbers $n$ for which
$$
\sigma(n)=\tau(n) \cdot\lceil\sqrt{n}\rceil .
$$
For a real number $x$, the notation $\lceil x\rceil$ denotes the smallest integer greater than or equal to $x$.
$$
\sigma(n)=\tau(n) \cdot\lceil\sqrt{n}\rceil .
$$
For a real number $x$, the notation $\lceil x\rceil$ denotes the smallest integer greater than or equal to $x$.