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: Time Limit Exceeded)

fn main() {
    let v = read();
    let ans = solve(v);
    write(ans);
}
 
fn read() -> i32 {
    let mut l1 = String::new();
    std::io::stdin().read_line(&mut l1).ok();
    let mut iter = l1.trim().split_whitespace();
    let n = iter.next().unwrap().parse::<i32>().unwrap();
    n
}
 
fn write(s: i32) {
    println!("{}", s);
}
 
fn solve(n: i32) -> i32 {
    fn yk(x: i32) -> Vec<i32> {
        let mut v: Vec<i32> = vec![];
        for i in 1..=x {
            if x % i == 0 {
                v.push(i);
            }
        }
        v
    }

    let mut w = 0;
    for i in 1..=n {
        w += i * yk(i).iter().count() as i32;
    }

    w
}