Divisor Loop

The inner loop jumps by i each time:

count = 0
for i in range(1, n + 1):
    for j in range(i, n + 1, i):
        count += 1

Implement count_divisor_steps(n) so it returns the final value of count.

Looping i from 1 to n is too slow for the largest inputs.

Examples

Example 1

Input:

count_divisor_steps(5)

Output:

10

5//1 + 5//2 + 5//3 + 5//4 + 5//5 = 5 + 2 + 1 + 1 + 1.

Example 2

Input:

count_divisor_steps(10)

Output:

27

Constraints

• 1 <= n <= 10**10
• An answer that loops n times will time out on the large tests.