
    Design a function for a learning management system that analyzes student assessment scores up to a given threshold to find and sum all pairs of complementary performance scores, where each score in a pair equals the sum of the proper divisors of the other score. The system uses these complementary score pairs to identify balanced learning relationships between students and optimize study group formations.
    

    
def amicable_numbers_sum(limit):
    """
    Design a function for a learning management system that analyzes student assessment scores up to a given threshold to find and sum all pairs of complementary performance scores, where each score in a pair equals the sum of the proper divisors of the other score. The system uses these complementary score pairs to identify balanced learning relationships between students and optimize study group formations.
    

    """
def amicable_numbers_sum(limit):
    """
    Design a function for a learning management system that analyzes student assessment scores up to a given threshold to find and sum all pairs of complementary performance scores, where each score in a pair equals the sum of the proper divisors of the other score. The system uses these complementary score pairs to identify balanced learning relationships between students and optimize study group formations.
    

    """
    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)