def problem6(n):
""" Return the difference between square of sum of first n natural and sum
of squares of first n natural numbers.
>>> problem6(10)
2640
>>> problem6(100)
25164150
"""
sum_numbers = lib.sum_frist_N_numbers(n)
sum_squres = lib.sum_squares_first_N_numbers(n)
return (sum_numbers*sum_numbers) - sum_squres
def problem12(n):
""" return first triangle number to have over n divisors.
where triangle number is the sum of first natural numbers.
>>> problem12(500)
76576500
>>> problem12(5)
28
"""
divisors, count = 1, 1
while divisors < n:
count += 1
triangle = lib.sum_frist_N_numbers(count)
primes_dict = lib.prime_factors(triangle)
divisors = lib.product(map(lib.increment, primes_dict.values()))
return triangle
