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)

#include <iostream>
#include <iomanip>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <vector>
#include <algorithm>
#include <numeric>
using namespace std;
#define IOS ios_base::sync_with_stdio(false);cin.tie(0)
#define endl "\n"
#define pb push_back
#define ff first
#define ss second
#define all(a) a.begin(),a.end()
#define int long long
const int MOD=1e9+7;
const int N=1e7+1;
int f[N];
int32_t main()
{
	IOS;
	int n;
	cin>>n;
	int sum=0;
	for(int i=1;i<=n;i++)
	{
		for(int j=1;j*i<=n;j++)
		{
			f[i*j]+=1;
		}	
	}
	for(int i=1;i<=n;i++)
		sum+=f[i]*i;
	cout<<sum<<endl;

	
}