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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

def divi(n):
    if n in prime: return 2
    sm=1
    for x in prime:
        token=0
        while n%x==0:
            n=n//x
            token+=1
        if token : sm*=(token+1)
        if n==1 : break
    return sm


n=int(input())
lst=[True for i in range(n+1)]
lst[0]=False
lst[1]=False

for i in range(2,n+1):
    if lst[i] :
        j=2*i
        while j<=n:
            lst[j]=False
            j+=i
prime=[i for i in range(n+1) if lst[i]]

sm=1
for i in range(2,n+1):
    sm+=i*divi(i)
print(sm)