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 Fortran (GNU Fortran 9.2.1) (judge verdict: Time Limit Exceeded)

program answer
  implicit none

  integer(8) :: N, i, sum

  read(*,*) N
  sum = 0
  do i = 1, N
     sum = sum + i*yaku(i)
  end do

  write(*,*) sum
  
  stop
contains
  integer(8) function yaku(x)
    implicit none

    integer(8) :: i, x, count

    count=0

    do i = 1, x
       if(mod(x,i)==0) then
          count = count + 1
       end if
    end do

    yaku=count
  end function yaku

  end program answer