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 PHP (7.4.4) (judge verdict: Time Limit Exceeded)

<?php
$n = intval(trim(fgets(STDIN)));
$counts = array_fill(1, $n, 1);
for($i = 2; $i <= $n; $i++){
  for($j = $i; $j <= $n; $j+=$i){
    $counts[$j]++;
  }
}
$sum = 0;
foreach($counts as $i => $c){
  $sum += $i*$c;
}
echo $sum;