New posts in Perfect Numbers

Why did the Egyptians not represent $2/3$ as a sum of unit fractions in the Rhind papyrus?

When $p$ is an odd prime, is $(p+2)/p$ an outlaw or an index?

Can a multi-perfect number be a perfect square?

If $N = q^k n^2$ is an odd perfect number and $n < q^{k+1}$, does it follow that $k > 1$?

Applications of Perfect Numbers

Can powers of primes be perfect numbers?

If $n$ is an even perfect number $ n> 6$ show that the sum of its digits is $\equiv 1 (\bmod 9)$

Discussion on even and odd perfect numbers.

Is there a similar formula like Ramanunjan's Eisenstein series identity for $\sum_{k=1}^{n-1}k^2 \sigma(k)\sigma(n-k)$?

Is there an odd integer $x < 105$ for which it is known that $x \nmid N$, if $N$ is an odd perfect number?