Question 163
Let $n \gt 4$ be a positive integer such that $n$ is composite (not a prime) and divides $\varphi(n)\sigma(n) + 1$, where $\varphi(n)$ is the Euler's totient function of $n$ and $\sigma(n)$ is the sum of the positive divisors of $n$. Prove that $n$ has at least three distinct prime factors.