<reponame>zlsun/ProjectEuler
#-*- encoding: utf-8 -*-
"""
Amicable numbers

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.
"""

from utils import *

N = 10000
L = N + 1
s = 0
m = [0] + [divisors_sum(i) - i for i in range(1, N + 1)]
for i in xrange(1, L):
    k = m[i]
    if k < i and m[k] == i:
        s += i + k
print s
# 31626

#-*- encoding: utf-8 -*-
"""
Amicable numbers

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.
"""

from utils import *

N = 10000
L = N + 1
s = 0
m = [0] + [divisors_sum(i) - i for i in range(1, N + 1)]
for i in xrange(1, L):
    k = m[i]
    if k < i and m[k] == i:
        s += i + k
print s
# 31626
#-*- encoding: utf-8 -*- Amicable numbers
 
 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. # 31626