Sum of subgroup indexes

This article defines an arithmetic function on groups
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Definition

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

$\sum _{H\leq G}[G:H]$

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

Equivalently it can be defined as:

$|G|\sum _{H\leq G}{\frac {1}{|H|}}$.