Question 70
A function $g: \mathbb{N} \rightarrow \mathbb{N}$ satisfies the following:
a. If $m$ is a proper divisor of $n$, then $g(m)\lt g(n)$.
b. If $m$ and $n$ are relatively prime and greater than $1$, then
$$
g(m n)=g(m) g(n)+(n+1) g(m)+(m+1) g(n)+m+n
$$
Find the least possible value of $g(2016)$.
a. If $m$ is a proper divisor of $n$, then $g(m)\lt g(n)$.
b. If $m$ and $n$ are relatively prime and greater than $1$, then
$$
g(m n)=g(m) g(n)+(n+1) g(m)+(m+1) g(n)+m+n
$$
Find the least possible value of $g(2016)$.