The inverse problem

The young mathematician Vasya continued his research in number theory. This time he studied the concept of greatest common divisor of two integers ($\gcd$). Recall that the $\gcd$ of two integers $a$ and $b$ is the largest integer by which both $a$ and $b$ are divisible without a remainder. Vasya calls a natural number $x$ good with respect to the natural number $n$, if \gcd(x, n) = x. For example, the good numbers with respect to $4$ are $1$, $2$, and $4$. Vasya calculated the count of good numbers with respect to $n$ and received the number $m$. But bad luck: he got so confused in his calculations that he could not remember the number for which he performed the computation. Help him find this value and determine the smallest number for which he could get such a response. It is known that the number for which Vasya carried out the calculations does not exceed 10^{18}.