Maximum prime divisor (functional)

#! /usr/bin/env python3

# The script calculates maximum prime divisor of a positive integer.
# Apart from input and output instructions the code's purely
# functional (as far as I can judge). The script may exceed the
# maximum recursion depth or make the interpreter freeze.

def divisorGenerator(a, b):
    return divisibilityCheck(a, a // (a // b + 1))

def divisibilityCheck(a, b):
    if a % b == 0:
        return primeCheck(a, b)
    else:
        return limitCheck(a, b)

def limitCheck(a, b):
    if b > 1:
        return divisorGenerator(a, b)
    else:
        return b

def primeCheck(a, b):
    if not [c for c in range(2, b // 2 + 1) if b % c == 0]:
        return b
    else:
        return limitCheck(a, b)

def intializer(a):
    return limitCheck(a, a // 2)

a = None
while not a:
    a = input("Enter a positive decimal integer to start evaluation or a non-number to exit: ")
    if a.isnumeric():
        try:
            print(intializer(int(a)))
        except:
            print("Ouch! This one didn't go down well!")

        a = None
    else:
        exit("Oh, well...")