def divisor_list(n):
"""Return the list of divisors of the given integer.
>>> divisor_list(24)
[1, 2, 3, 4, 6, 8, 12, 24]
>>> divisor_list(30850)
[1, 2, 5, 10, 25, 50, 617, 1234, 3085, 6170, 15425, 30850]
>>> divisor_list(math.factorial(5))
[1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120]
"""
factors = A5.factor_map(n)
factor_powers = (tuple(factor ** exp for exp in range(multiple + 1)) for factor, multiple in factors.items())
return sorted(reduce(operator.mul, data) for data in itertools.product(*factor_powers))
def divisor_count(n):
"""Compute the number of divisors for the given integer.
>>> divisor_count(7)
2
>>> divisor_count(12)
6
>>> divisor_count(36)
9
>>> divisor_count(math.factorial(5))
16
>>> divisor_count(math.factorial(15))
4032
"""
# Each divisor is a product of multiples of each prime factor.
factor_counts = A5.factor_map(n).values()
# Compute the product of factor counts, incrementing since a factor may
# be taken to the 0th power.
return reduce(operator.mul, (1 + count for count in factor_counts), 1)
