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 input::Input;

fn main() {
    let mut input = Input::default();

    let n = input.parse();

    let mut ans = 0;
    for i in 1..=n {
        ans += i * g((n + i) / i);
    }
    println!("{}", ans);
}

fn g(n: u64) -> u64 {
    n * (n - 1) / 2
}

#[allow(dead_code)]
pub mod input {
    #[derive(Default)]
    pub struct Input(Vec<String>);

    impl Input {
        pub fn read_line(&mut self) -> String {
            let mut s = String::new();
            std::io::stdin().read_line(&mut s).ok().expect("read error");
            s
        }
        pub fn parse<T: std::str::FromStr>(&mut self) -> T {
            let x = if let Some(x) = self.0.pop() {
                x
            } else {
                let s = self.read_line();
                self.0 = s.split_whitespace().map(String::from).rev().collect();
                self.0.pop().expect("reached EOF")
            };
            x.parse().ok().expect("parse error")
        }
    }
}