p21.py

"""


Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers.

For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.

Evaluate the sum of all the amicable numbers under 10000.

"""
def d(n):
    sum=0
    n=int(n)
    for i in range(2,int(n/2)+1):
        if n%i==0:
            if n/i <= i:
                break
            sum=sum+i+n/i
        
    return int(sum+1)

isami = []
sum=0
for i in range(2,10000):
    if i in isami:
        continue
    dn=d(i)
    if (i!= dn) and (i == d(dn)):
        isami.append(i)
        isami.append(dn)
        sum=sum+i+dn
        print(i)
        print(dn)
print(sum)