The proper divisors of a natural number $n$ are those factors of $n$ that are less than $n$. For example, the proper divisors of 10 are 1, 2, and 5. If the sum of the proper divisors of $n$ is larger than $n$ then $n$ is said to be abundant . If the sum is less than $n$ then $n$ is deficient . If the sum equals $n$, then $n$ is perfect .
For example, the proper divisors of 10 add to 1+2+5=8 and so 10 is deficient. The proper divisors of 12 add to 1+2+3+4+6 = 16, and so 12 is abundant. The proper divisors of 6 add to 1+2+3 = 6, and so 6 is perfect.
Perfect numbers have been studied for more than 2,000 years. It is still unknown how many perfect numbers exist. At present only 39 are known and the largest of them has 18,669,112 digits.
Find the smallest perfect number greater than 6 and enter it here .