
    Design a system that analyzes student performance patterns by finding pairs of assessment scores where the sum of proper divisors of one score equals the other score and vice versa (up to a specified maximum score threshold), and calculate their total to determine optimal difficulty adjustment ranges. The analysis should only consider score pairs below the given threshold where both scores form this special reciprocal relationship. The system will use this sum to automatically calibrate future assessment difficulties.
    

    
def amicable_numbers_sum(limit):
    """
    Design a system that analyzes student performance patterns by finding pairs of assessment scores where the sum of proper divisors of one score equals the other score and vice versa (up to a specified maximum score threshold), and calculate their total to determine optimal difficulty adjustment ranges. The analysis should only consider score pairs below the given threshold where both scores form this special reciprocal relationship. The system will use this sum to automatically calibrate future assessment difficulties.
    

    """
def amicable_numbers_sum(limit):
    """
    Design a system that analyzes student performance patterns by finding pairs of assessment scores where the sum of proper divisors of one score equals the other score and vice versa (up to a specified maximum score threshold), and calculate their total to determine optimal difficulty adjustment ranges. The analysis should only consider score pairs below the given threshold where both scores form this special reciprocal relationship. The system will use this sum to automatically calibrate future assessment difficulties.
    

    """
    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)