Problem:
Score : 400 points

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.

Solution in Rust (1.42.0) (judge verdict: Accepted)

fn main() {
    proconio::input! {
        n:usize
    }
    let mut ans = 0;
    //    let mut i = 1;
    let s = (n as f64).sqrt() as usize;
    let mut i = 1;
    while i * i <= n {
        let c = n / i;
        ans += i * c * (c + 1) / 2;
        // さらに、c について、いくつかまとめて計算。
        if c > i {
            let d = n / (i + 1);
            ans += (c * (c + 1) - d * (d + 1)) * i * (i + 1) / 4;
        }
        i += 1;
    }
    println!("{}", ans);
}