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)

use proconio::{input, fastout};

#[fastout]
fn main() {
    input! { n: i64 }

    let mut a: Vec<i64> = vec![0; 10000001];
    for i in 1..n + 1 {
        let mut j = 1;
        while i * j <= n {
            a[(i * j) as usize] += 1;
            j += 1;
        }
    }

    let mut ans: i64 = 0;
    for i in 1..n + 1 {
        ans += i * (a[i as usize]);
    }
    println!("{}", ans);
}