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 n = read_int ()
let n' = int_of_float (sqrt (float_of_int n)) + 1

let rec solve k ans =
  if k = n' then ans
  else
    let k' = n / k in
    let f = k' * k' + k' - k * k in
    solve (k + 1) (ans + k * f)

let () = Printf.printf "%d\n" (solve 1 0)