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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;
 
public class Main {
	Scanner sc = new Scanner(System.in);
	final int MOD = (int)1e9 + 7;
	final int MAX = Integer.MAX_VALUE;
	final long LMAX = Long.MAX_VALUE;
	int len = (int)1e7;
	
	
	void doIt() {
		int N = sc.nextInt();
		long[] num = new long[N + 1];
		Arrays.fill(num, 2);
		num[1] = 1;
		for(int i = 2; i <= N; i++) {
			for(int j = i * 2; j <= N; j += i) {
				num[j]++;
			}
		}
		long sum = 0;
		for(int i = 1; i <= N; i++) {
			sum += i * num[i];
		}
		System.out.println(sum);
		//System.out.println(Arrays.toString(num));
	}
	
	public static void main(String[] args) {
		new Main().doIt();
	}
 
}