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 OCaml (4.10.0) (judge verdict: Accepted)

let () =
  Scanf.scanf "%d" @@ fun n ->
  let h x = x * (x + 1) / 2 in
  let rec g i a =
    if i > n then a
    else g (i + 1) (a + i * (h (n / i))) in  
  Printf.printf "%d" (g 1 0)