from time import time, sleep

#my fastest version up to now
def proper_divisors_sum1(n):
    pd_list = []
    for x in range(1, int(n**.5)+1):
        if n % x == 0:
            pd_list.append(x)
            pd_list.append(n//x)
    pd_list = list(set(pd_list))
    pd_list.sort()
    pd_list = pd_list[:-1]
    return sum(pd_list)


#This uses several of Martin's ideas
#It's now my fastest version
def proper_divisors_sum2(n):
    pd = set((1,))
    for x in range(2, int(n**.5)+1):
        if n % x == 0:
            pd.update((x, n//x))
    return sum(list(pd))


# This incorporates all of Martin's ideas
# Seems that divmod() is a speed killer
def proper_divisors_sum3(n):
    pd = set((1,))
    for x in range(2, int(n**.5)+1):
        factor, mod = divmod(n,x)
        if mod == 0:
            pd.update((x,factor))
    return sum(list(pd))


n = 100000
m = 100000  #number of loops
sleep_secs = 1


t0 = time()
for i in range(m):
    sum_ = proper_divisors_sum1(n)
t1 = time()
print("time1 =", round((t1-t0), 3))

sleep(sleep_secs)

t0 = time()
for i in range(m):
    sum_ = proper_divisors_sum2(n)
t1 = time()
print("time2 =", round((t1-t0), 3))

sleep(sleep_secs)

t0 = time()
for i in range(m):
    sum_ = proper_divisors_sum3(n)
t1 = time()
print("time3 =", round((t1-t0), 3))

"""
time1 = 8.999
time2 = 7.924
time3 = 13.959
"""