The nonexistence conjecture for odd perfect numbers

An integer $n$ is perfect if the sum of its positive proper divisors equals $n$. The known even perfect numbers have the form $2^{r-1}(2^r-1)$ when $2^r-1$ is prime.

Odd perfect number conjecture. There are no odd perfect numbers.

No odd perfect number is currently known, while the existence or nonexistence of such numbers remains an open problem.