Perfect numbers (prime number theory) Calculate x and y, so that $2 ^ x. 3 ^ y$ be a perfect number.
I tried to produce using this formula of the sum of the divisors of a number: Let $a ^ x, b ^ y,$ and  $c ^ z$ prime factors of a number: $\frac{ a^{x+1} -1}{ a-1}. \frac{b^{y-1} -1}{b-1}. \frac{c^{c +1} -1}{c-1}$
It replaces $ 2 ^ x = a$ and $ 3^y = b $, but it can't produce much else: $ a.b $ = $ \frac {(2a-1) (3b-1)} {2} $

An even number is perfect if and only if it is of the form $2^{n-1}(2^n-1)$ for some $n$ with $2^n-1$ being prime. And $2^n-1=3^m$ is prime only for $n=2$ and $m=1$. So we obtain $2^1\cdot 3^1=6$.
