from math import gcd

def max_gcd_sum(arr):
    n = len(arr)
    arr.sort(reverse=True)
    odd_gcd, even_gcd = arr[0], arr[1]
    for i in range(2, n):
        if i % 2 == 0:
            even_gcd = gcd(even_gcd, arr[i])
        else:
            odd_gcd = gcd(odd_gcd, arr[i])
    return odd_gcd + even_gcd