Collatz-problem

[CaptainNeemo]

Dear forum,
I got a question to my function below:
The problem is the return value of tau() is integer usually, but if I call tau() from test() the return value is None and not writable into my dictionary. Maybe you got an idea on how to solve this problem. Also as I am a python beginner I am open to any tips and considerations for the future.

def tau(i,count=0):
    """
    This function counts how many times it has to iterate a number to become 1. Its the function of the Collatz-Problem with a memory.
    """
    if i < 1:
        raise ValueError("n muss >=1 sein")
    if i in tau.cache:
        return count + tau.cache[i]
    else:
        tau(i // 2 if i % 2 == 0 else i * 3 + 1, count + 1)

tau.cache = {1: 0}

def test(N):
    """ 
    This function should write the value between 2 and N and his number of iterations into a dictionairy. 
    """
    for k in range(2,N):
        tau.cache[k] = tau(k)
    print(tau.cache)