Sum of subgroup indexes

This article defines an arithmetic function on groups
View other such arithmetic functions

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:

$\left|G\right|{\sum }_{H\le G}\frac{1}{\left|H\right|}$.