
    Given the total number of user interactions on a social media post, find the sum of all even-numbered engagement patterns that perfectly divide the total interaction count, as these patterns represent balanced sharing behaviors in the content recommendation system. These symmetric engagement factors are crucial for understanding content virality and optimizing distribution strategies across the social network.
    

    
import math

def sumofFactors(n):
    """
    Given the total number of user interactions on a social media post, find the sum of all even-numbered engagement patterns that perfectly divide the total interaction count, as these patterns represent balanced sharing behaviors in the content recommendation system. These symmetric engagement factors are crucial for understanding content virality and optimizing distribution strategies across the social network.
    

    """
import math

def sumofFactors(n):
    """
    Given the total number of user interactions on a social media post, find the sum of all even-numbered engagement patterns that perfectly divide the total interaction count, as these patterns represent balanced sharing behaviors in the content recommendation system. These symmetric engagement factors are crucial for understanding content virality and optimizing distribution strategies across the social network.
    

    """
    if n % 2 != 0:
        return 0
    res = 1
    for i in range(2, int(math.sqrt(n)) + 1):
        count = 0
        curr_sum = 1
        curr_term = 1
        while n % i == 0:
            count = count + 1
            n = n // i
            if i == 2 and count == 1:
                curr_sum = 0
            curr_term = curr_term * i
            curr_sum = curr_sum + curr_term
        res = res * curr_sum
    if n >= 2:
        res = res * (1 + n)
    return res