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() {
    let n: i32 = read();
    println!("{}", solve(n));
}

fn read<T: std::str::FromStr>() -> T {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).ok();
    buf.trim().parse().ok().unwrap()
}

fn solve(n: i32) -> i64 {
    let mut counts: Vec<i32> = std::iter::repeat(0).take(n as usize + 1).collect();
    for i in 1..=n {
        for j in (i..=n).step_by(i as usize) {
            counts[j as usize] += 1;
        }
    }

    counts
        .iter()
        .enumerate()
        .map(|(i, &c)| (i as i64) * (c as i64))
        .sum()
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_solve_1() {
        assert_eq!(23, solve(4));
    }

    #[test]
    fn test_solve_2() {
        assert_eq!(26879, solve(100));
    }

    #[test]
    fn test_solve_3() {
        assert_eq!(838627288460105, solve(10000000));
    }
}