def problem_12():
"""
The sequence of triangle numbers is generated by adding the natural numbers.
So the 7^(th) triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:
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?
"""
i = 1
t = 0
while True:
d = len(elib.divisors(t))
if len(elib.divisors(t)) > 500:
return t
t += i
i += 1
def 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.
"""
admicables = []
for i in xrange(1, 10000):
di = sum(elib.divisors(i)[:-1])
if i == di:
continue
dii = sum(elib.divisors(di)[:-1])
if i == dii:
admicables.append(i)
admicables.append(di)
return sum(set(admicables))
