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;

class Program
{
	static void Main(string[] args)
	{
		int i;

		int n = int.Parse(Console.ReadLine());
		Int64[] fk = new Int64[n+1];

		int tmpk;
		Int64 result = 0;

		for (i = 1; i <= n; i++)
		{
			tmpk = i;
			while(tmpk <= n)
            {
				fk[tmpk]++;
				tmpk += i;
            }
			result += (Int64)i * fk[i];
		}


		Console.WriteLine(result);

		return;
	}
}