
    Design an algorithm for an adaptive learning system that identifies and sums all pairs of complementary skill levels where the sum of proper divisors of one skill level equals the other skill level and vice versa, up to a maximum difficulty threshold. This relationship analysis helps determine optimal student progression paths through interconnected learning modules.
    

    
def amicable_numbers_sum(limit):
    """
    Design an algorithm for an adaptive learning system that identifies and sums all pairs of complementary skill levels where the sum of proper divisors of one skill level equals the other skill level and vice versa, up to a maximum difficulty threshold. This relationship analysis helps determine optimal student progression paths through interconnected learning modules.
    

    """
def amicable_numbers_sum(limit):
    """
    Design an algorithm for an adaptive learning system that identifies and sums all pairs of complementary skill levels where the sum of proper divisors of one skill level equals the other skill level and vice versa, up to a maximum difficulty threshold. This relationship analysis helps determine optimal student progression paths through interconnected learning modules.
    

    """
    if not isinstance(limit, int):
        return 'Input is not an integer!'
    if limit < 1:
        return 'Input must be bigger than 0!'
    amicables = set()
    for num in range(2, limit + 1):
        if num in amicables:
            continue
        sum_fact = sum([fact for fact in range(1, num) if num % fact == 0])
        sum_fact2 = sum([fact for fact in range(1, sum_fact) if sum_fact % fact == 0])
        if num == sum_fact2 and num != sum_fact:
            amicables.add(num)
            amicables.add(sum_fact2)
    return sum(amicables)