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<bits/stdc++.h>
#define ll long long
#define IOS ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)
using namespace std;
ll z=1000000000+7;
ll f[10000001]={0};
void nod(ll n)
{
  for(ll i=1;i<=n;i++)
  {
    f[i]=2;
  }
  f[1]=1;
  for(ll i=2;i<=n;i++)
  {
    for(ll j=2*i;j<=n;j+=i)
    {
      f[j]=f[j]+1;
    }
  }
}

int main()
{
  IOS;
  ll t=1;
  //cin>>t;
  while(t--)
  {
    ll i,n,k,sum=0,x,p=0,l,r,ans=0,cnt=0,m,j;
    cin>>n;
    nod(n);
    ans=0;
    for(i=1;i<=n;i++)
    {
      ans+=i*f[i];
    }
    cout<<ans;
  }
    return 0;
}