Anti-Divisors of a Number

The anti-divisors are numbers that do not divide a given number by the largest possible margin, and they can be found following a simple set of rules:

• Every number greater than 1 and lower than n is checked.
• Every checked number must not be a divisor of n.
• If the checked number is odd and it is a divisor of n * 2 - 1 or n * 2 + 1 it's an anti-divisor.
• If the checked number is even and it is a divisor of n * 2, it's an anti-divisor.

Given an integer n, implement a function that returns a list containing the anti-divisors of n sorted in ascending order.

Examples

anti_divisors(10) ➞ [3, 4, 7]
# 3 is a divisor of 21 (10 * 2 + 1)
# 4 is a divisor of 20 (10 * 2)
# 7 is a divisor of 21

anti_divisors(12) ➞ [5, 8]
# 5 is a divisor of 25 (12 * 2 + 1)
# 8 is a divisor of 24 (12 * 2)

anti_divisors(20) ➞ [3, 8, 13]
# 3 is a divisor of 39 (20 * 2 - 1)
# 8 is a divisor of 40 (20 * 2)
# 13 is a divisor of 39

Notes

The given n can be any integer, either positive, negative or 0.