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 sum = ref 0 in
  let dp = Array.make (n + 1) 0 in
  for i = 1 to n do
    let rec iter j =
      if j <= n then (dp.(j) <- j + dp.(j); iter (i + j)) in
    iter i;
    sum := !sum + dp.(i);
  done;
  Printf.printf "%d\n" !sum