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++ (GCC 9.2.1) (judge verdict: Accepted)

/**
 *    Author  : Ador
 *    Created : 24.07.2020
**/
#include <iostream>
#include <cstdio>
#include <iomanip>
#include <algorithm>
#include <string>
#include <cstring>
#include <sstream>
#include <cmath>
#include <cstdlib>
#include <cctype>
typedef long long int ll ;
typedef unsigned long long int ull ;
using namespace std ;
int main(void)
{
    ios_base::sync_with_stdio(false) ; cin.tie(0) ; cout.tie(0) ;
        //freopen("input.txt", "r", stdin) ;
        //freopen("output.txt", "w", stdout) ;
    ll n , i , sum = 0 ; cin >> n ;
    for(i = 1 ; i <= n ; ++i)
    {
        ll x = (n / i) ;
        sum += i * ((x * (x + 1)) / 2) ;
    }
    cout << sum << "\n" ;
    return 0 ;
}