Subtracting proper divisors

Given an integer n, we apply the following process:
- search the largest proper divisor of n
- subtract this number from n
- repeat until we reach 1

Let f(n) the number of steps before reaching 1.

Example with n = 30

• n = 30 - 15 (15 = Largest proper divisor of 30)
• n = 15 - 5 (5 = Largest proper divisor of 15)
• n = 10 - 5 (5 = Largest proper divisor of 10)
• n = 5 - 1 (1 = Largest proper divisor of 5)
• n = 4 - 2 (2 = Largest proper divisor of 4)
• n = 2 - 1 (1 = Largest proper divisor of 2)
• n = 1 Stop => f(30) = 6

Find f(1000000!) // Factorial(1000000)

[My timing: 6 sec]