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 = read::<i64>()[0];
  
  let mut sum = 0;
  for k in 1..=n {
    sum += k*(1+n/k)*(n/k)/2;
  };
  
  println!("{}", sum);
}

fn read<T: std::str::FromStr>() -> Vec<T> {
  gets().split_whitespace().filter_map(|s|s.parse().ok()).collect()
}

fn gets() -> String {
  let mut line = String::new();
  std::io::stdin().read_line(&mut line).ok();
  line.trim().to_string()
}