
    Design a function that determines the total number of shared performance benchmarks between two test score thresholds, where benchmarks are defined as factors that evenly divide both scores, to help establish balanced difficulty intervals for future assignments. The function should analyze two input test score thresholds and calculate the sum of all their common divisors to identify optimal breakpoints for assignment complexity adjustments.
    

    
def sum(a, b):
    """
    Design a function that determines the total number of shared performance benchmarks between two test score thresholds, where benchmarks are defined as factors that evenly divide both scores, to help establish balanced difficulty intervals for future assignments. The function should analyze two input test score thresholds and calculate the sum of all their common divisors to identify optimal breakpoints for assignment complexity adjustments.
    

    """
def sum(a, b):
    """
    Design a function that determines the total number of shared performance benchmarks between two test score thresholds, where benchmarks are defined as factors that evenly divide both scores, to help establish balanced difficulty intervals for future assignments. The function should analyze two input test score thresholds and calculate the sum of all their common divisors to identify optimal breakpoints for assignment complexity adjustments.
    

    """
    sum = 0
    for i in range(1, min(a, b)):
        if a % i == 0 and b % i == 0:
            sum += i
    return sum