Notice that $\sigma(p^{k-1}) = k$ and so the image of $\sigma$ is all of $\mathbb{N}$.
By the way, $\sigma$ is usually used for the sum of divisors function, and it is more standard to use $d$ or $\tau$ for your function.
Notice that $\sigma(p^{k-1}) = k$ and so the image of $\sigma$ is all of $\mathbb{N}$.
By the way, $\sigma$ is usually used for the sum of divisors function, and it is more standard to use $d$ or $\tau$ for your function.