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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.
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"""
from ProjectEuler.helper_functions import HelperFunctions as Hf
d = {}
for n in range(1, 10000):
divisors = Hf.divisors(n)
divisors.remove(n)
d[n] = sum(divisors)
s = 0
for n in range(1, 10000):
a = n
b = d[n]
if b in d:
a2 = d[b]
if a2 == a and a != b:
s += a2 + a
print s/2
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
Let us list the factors of the first seven triangle numbers:
1: 1
3: 1,3
6: 1,2,3,6
10: 1,2,5,10
15: 1,3,5,15
21: 1,3,7,21
28: 1,2,4,7,14,28
We can see that 28 is the first triangle number to have over five divisors.
What is the value of the first triangle number to have over five hundred divisors?
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"""
from time import clock
from ProjectEuler.helper_functions import HelperFunctions as Hf
clock()
i = 1
s = i
while True:
i += 1
s += i
print s
if Hf.number_of_divisors(s) >= 500:
break
print s
print clock()