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: Wrong Answer)

program d172

integer :: i, j, n, m
integer :: p(2:10000000)
integer(16) :: k, z, f

p(:) = 1
m = 1
z = 0

read *, n

do while (n > 1)
 do i = 2, n
 if (mod(n,i) == 0) then
  p(i) = p(i) + 1
  n = n / p(i)
  if(i > m) then
   m = i
  end if
  cycle
 end if
 end do
end do

do i = 1, n
 do j = 2, m
  f = f * p(j)
 end do
 k = f * i
 z = z + k
end do

print *, z

end program d172