A12082 | Fun with Integers

You are given a positive integer $n$ greater or equal to $2$ . For every pair of integers $a$ and $b$ ( $2 \le |a|, |b| \le n$ ), you can transform $a$ into $b$ if and only if there exists an integer $x$ such that $1 < |x|$ and ( $a \cdot x = b$ or $b \cdot x = a$ ), where $|x|$ denotes the absolute value of $x$ .

After such a transformation, your score increases by $|x|$ points and you are not allowed to transform $a$ into $b$ nor $b$ into $a$ anymore.

Initially, you have a score of $0$ . You can start at any integer and transform it as many times as you like. What is the maximum score you can achieve?

A single line contains a single integer $n$ ( $2 \le n \le 100\,000$ ) — the given integer described above.

Print an only integer — the maximum score that can be achieved with the transformations. If it is not possible to perform even a single transformation for all possible starting integers, print $0$ .