Question 51
An integer is a perfect number if and only if it is equal to the sum of all of its divisors except itself. For example, $28$ is a perfect number since $28 = 1 + 2 + 4 + 7 + 14$.
Let $n!$ denote the product $1 \cdot 2 \cdot 3 \cdots n$, where $n$ is a positive integer. An integer is a factorial if and only if it is equal to $n!$ for some positive integer $n$. For example, $24$ is a factorial number since $24 = 4! = 1 \cdot 2 \cdot 3 \cdot 4$.
Find all perfect numbers greater than $1$ that are also factorials.
Let $n!$ denote the product $1 \cdot 2 \cdot 3 \cdots n$, where $n$ is a positive integer. An integer is a factorial if and only if it is equal to $n!$ for some positive integer $n$. For example, $24$ is a factorial number since $24 = 4! = 1 \cdot 2 \cdot 3 \cdot 4$.
Find all perfect numbers greater than $1$ that are also factorials.