101723: [AtCoder]ABC172 D - Sum of Divisors

Problem Statement

For a positive integer $X$, let $f(X)$ be the number of positive divisors of $X$.

Given a positive integer $N$, find $\sum_{K=1}^N K\times f(K)$.

Constraints

• $1 \leq N \leq 10^7$

Input

Input is given from Standard Input in the following format:

$N$

Output

Print the value $\sum_{K=1}^N K\times f(K)$.

Sample Input 1

4

Sample Output 1

23

We have $f(1)=1$, $f(2)=2$, $f(3)=2$, and $f(4)=3$, so the answer is $1\times 1 + 2\times 2 + 3\times 2 + 4\times 3 =23$.

Sample Input 2

100

Sample Output 2

26879

Sample Input 3

10000000

Sample Output 3

838627288460105

Watch out for overflows.