math problem using recursion?

[Gribouillis]

You could use recursion to build the tree. The key is to suppose that the problem is solved. Let func() be a function that takes a number as argument and returns None if it is not a semi-prime or the root of this semi-prime's tree if it is a semi-prime.

We need to define what the root of a tree will be. We'll take a tuple ((factor0, factor1), (subroot0, subroot1)). For this we could use a namedtuple. Here is an algorithm

Root = namedtuple('Root', 'factor subroot')

def func(number):
    try:
        fac0, fac1 = decompose_semi_prime_in_factors(number)
    except NotSemiPrime:
        return None
    root0 = func(int(f'{fac0}{fac1}'))
    root1 = None
    if fac0 != fac1:
        root1 = func(int(f'{fac1}{fac0}'))
    return Root((fac0, fac1), (root0, root1))