Let $N = q^k n^2$ be an odd perfect number with special/Eulerian prime $q$ satisfying $q \equiv k \equiv 1 \pmod 4$ and $\gcd(q,n)=1$. Denote the Euler-totient function of the positive integer $x$ by $\varphi(x)$, and the classical sum of divisors of $x$ by $\sigma(x)=\sigma_1(x)$. MOTIVATION Fr...

This is my attempt at the Collatz Conjecture! Not so bold to say it's correct, I just would like to know where the error is, thanks! The Collatz Conjecture states that whatever $n \in \mathbb{N}$ follows this algorithm: ${\displaystyle f(n)={\begin{cases}{\frac {n}{2}},&{\text{if }}n{\text{ even}...