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 std::collections::HashMap;

macro_rules! get_one {
    ($t:ty) => {{
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        line.trim().parse::<$t>().unwrap()
    }};

    ($t:ty; $n:expr) => {
        (0..$n).map(|_| get_one!($t)).collect::<Vec<_>>()
    };
}

fn main() {
    let n = get_one!(usize);


    let v: usize = (1..=n).into_iter().map(|m| sum_till_n(m, n)).sum();

    println!("{}", v);



}

fn sum_till_n(m: usize, n: usize) -> usize {
    let mut i = 0;
    let mut sum = 0;
    while i <= n {
        sum += i;
        i += m;
    }
    sum
}