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Questions about or involving perfect numbers which are positive integers that are equal to the sum of their proper positive divisors.

A positive integer $n$ is said to be a perfect number if it is equal to the sum of its proper positive divisors.

The smallest example of a perfect number is $6$ as it has positive proper divisors $1$, $2$, $3$, and $1 + 2 + 3 = 6$.

More generally, $2^{p-1}(2^p-1)$ is perfect whenever $2^p - 1$ is a prime (called a Mersenne prime); the case above corresponds to $p = 2$. Furthermore, every even perfect number is of this form.

It is currently unknown whether there are infinitely many perfect numbers or whether any odd perfect numbers exist.

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