def euler012(n):
''' Highly divisible triangular number
The sequence of triangle numbers is generated by adding the natural numbers.
So the 7th 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?
>>> euler012(5)
28
>>> euler012(500)
76576500
'''
return dropwhile(lambda x: len(list(divisors(x))) <= n, gentriangle()).next()
def euler012b(n):
''' Original version of above function.
>>> euler012b(5)
28
>>> euler012b(500)
76576500
'''
t = gentriangle()
while True:
triangle = t.next()
if len(list(divisors(triangle))) > n:
return triangle
def euler005(n):
''' Smallest multiple
2520 is the smallest number that can be divided by each of the numbers from 1 to
10 without any remainder.
What is the smallest positive number that is evenly divisible by all of the numbers
from 1 to 20?
>>> euler005(10)
2520
>>> euler005(20)
232792560
'''
start = 1
multiply = range(2, n+1) # steps through each integer in the range.
for i in multiply:
if start % i != 0:
try:
start = start * list(divisors(i))[1] # multiplies by the smallest factor
except IndexError:
start = start * i # if is prime, multiply by that number
return start
def ami(n):
return sum(divisors(n, inclusive=False))
