Sum of subgroup indexes

Definition
Let $$G$$ be a finite group. The sum of subgroup indices of $$G$$ is the sum:

$$\sum_{H \le G} [G:H]$$

In other words, it is the sum, over all subgroup of $$G$$, of the index of that subgroup.

Equivalently it can be defined as:

$$|G| \sum_{H \le G} \frac{1}{|H|}$$.