Definition

The arithmetic function $d(n)$ counts the number of positive divisors of $n$ and is defined as $$d(n)=\prod_{i=1}^{k}(\alpha_{i}+1)$$where we recall by the Fundamental Theorem of Arithmetic that $$n=\prod_{i=1}^{k}p_{i}^{\alpha_{i}}$$ ## Note $d(n)$ is Multiplicative.