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 atcoder
implicit none
integer :: n , i , num , f1 , yakusuu
read *, n
num = 0
do i = 1 , n
  f1 = yakusuu(i)
  num = num + f1 * i
end do
print *,num
end program atcoder

function yakusuu(n)
implicit none
integer :: n , yakusuu , i
yakusuu = 0
do i = 1 , n
  if(mod(n,i) == 0)then
    yakusuu = yakusuu + 1
  end if
end do
end function yakusuu