Let f, g: N -{1} → N be functions defined by f(a)=α, where α is the maximum of the powers of those primes p such that p^α divides a, and g(a)=a+1,…

Let $\displaystyle f, g: \mathbb{N}-\{1\} \rightarrow \mathbb{N}$ be functions defined by $\displaystyle f(a)=\alpha$, where $\displaystyle \alpha$ is the maximum of the powers of those primes $\displaystyle p$ such that $\displaystyle p^\alpha$ divides $\displaystyle a$, and $\displaystyle g(a)=a+1$, for all $\displaystyle a \in \mathbb{N}-\{1\}$. Then, the function $\displaystyle f+g$ is