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 C# (Mono-mcs 6.8.0.105) (judge verdict: Time Limit Exceeded)

using System;
class Program
{
  static void Main(string[] args)
  {
    int n = int.Parse(Console.ReadLine());
    int r = 0;
    for(int i=1; i<=n; i++)
    {
      r += i * SumOfDivisor(i);
    }
    Console.WriteLine(r);
  }
  static int SumOfDivisor(int s)
  {
    int r = 0;
    for(int i=1; i<=s; i++)
    {
      if(s % i == 0)
      {
        r++;
      }
    }
    return r;
  }
}