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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;


namespace ABC172Test
{
    class Program
    {
        static void Main()
        {
            int N = int.Parse(Console.ReadLine().Trim());
            long result = 0;
            result = abc172_f3(N);
            Console.WriteLine(result);
        }
        
        static long abc172_f3(int k)
        {
            long sum = 0;
            for (int i = 1; i <= k; i++)
            {
                int max = k / i;
                sum += (((long)max * ((long)max + 1) / 2) * (long)i);
            }
            return sum;
        }

    }

}