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: Accepted)

program sample
    implicit none
  
    integer(8) :: i,j,m,n,a(10000000)
    
    integer(8),allocatable :: x(:),y(:)
  
    read(*,*) n

    do i=1,10000000
        a(i)=0
    end do
    do i=1,n
        do j=1,n/i
             a(i*j)=a(i*j)+1
         end do
    end do
    m=0
    do i=1,n
        m=m+a(i)*i

    end do
    write(*,*) m
  
    stop
end program sample