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 Perl (5.26.1) (judge verdict: Accepted)

my $N = <>;
my $sum =0;
for(my $i=1;$i<=sqrt($N);$i++){
    my $j = int($N/$i);
    $sum +=  $i*($j*($j+1)/2 ); 
    if($i!=$j){
      my $k = int($N/($i+1)); 
      $sum +=  ($i*($i+1)/2)* ($j*($j+1)/2 - $k*($k+1)/2); 
    }
}    
print "$sum";