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 M24
 implicit none
 integer::N=0,ishota=0,ishotb=0,s=0,f=0
 real::b=0
 read(*,*)N
 do ishota=1,N
  f=0
  do ishotb=1,ishota
   b=mod(ishota,ishotb)
   if(b==0)then
    f=f+1
   end if
  end do
  s=s+ishota*f
 end do
 print'(i0)',s
end program M24