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