欧拉计划(python) problem 21

Amicable numbers

Problem 21

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.

python code:

import math

sqrt=math.sqrt

def func(x):

result=1

k=int(sqrt(x))+1

for i in range(2,k):

if x%i==0 and i!=sqrt(x):

result+=i+x/i

else:

if (x%i==0 and i==sqrt(x)):

result+=i

return result

result=0

for i in range(4,10001):

k=func(i)

if k!=i and func(k)==i:

result+=i

print(result)

time : <1s