After delivering all the Christmas presents, Santa finally have some leisure time to study Mathematics, which is his favourite hobby. Santa defines a positive integer n as a “Christmas number” if $n$ is a divisor of $\phi (n) \sigma (n) + 1$. Santa challenges Rudolph the red nosed reindeer and asks him to find two prime numbers such that their product is a “Christmas number”. Is it possible for Rudolph to do so? Prove your claim. Note: $\sigma (n)$ denotes the sum of positive divisors of $n$. $\phi (n)$ denotes the Euler’s totient function of $n$, which counts the positive integers up to $n$ that are relatively prime to $n$.