Question
Sum of Divisor Totals
Ethan is exploring numbers and their divisors. Given a positive integer N, he wants to calculate the total sum of divisors for every number from 1 to N. For each number i, he defines F(i) as the sum of all divisors of i. Ethan’s goal is to find the combined value of F(i) for all numbers from 1 to N. Can you help him compute this total sum?
Input
The first line of the input contains a single integer N.
Constraints
1 ≤ n ≤ 106
Constraints
1 ≤ n ≤ 106
Output
Print the required answer.
Example
Sample Input
4
Sample Output
15
Explanation
F(1) = 1
F(2) = 1 + 2 = 3
F(3) = 1 + 3 = 4
F(4) = 1 + 2 + 4 = 7
ans = F(1) + F(2) + F(3) + F(4) = 1 + 3 + 4 + 7 = 15
4
Sample Output
15
Explanation
F(1) = 1
F(2) = 1 + 2 = 3
F(3) = 1 + 3 = 4
F(4) = 1 + 2 + 4 = 7
ans = F(1) + F(2) + F(3) + F(4) = 1 + 3 + 4 + 7 = 15