def square_lams(upperlimit):
divfours = [i for i in range(upperlimit + 1) if i % 4 == 0 and i > 4]
total = 0
for num in divfours:
total += len([d for d in divisors_gen(num // 4)]) // 2
return total
def p174():
divfours = [i for i in range(1000000 + 1) if i % 4 == 0 and i > 4]
total = 0
for num in divfours:
num_lams = len([d for d in divisors_gen(num // 4)]) // 2
if 0 < num_lams < 11:
total += 1
return total
def p012():
cur_tri = 1
maxmax = 1
i = 1
while maxmax < 500:
i += 1
cur_tri += i
numDivs = sum(1 for _ in divisors_gen(cur_tri))
if numDivs > maxmax:
maxmax = numDivs
return cur_tri
def prime_factors_gen(n: int) -> Iterator[Any]:
"""prime factors generator
:param n: number to be factorized
:type n: int
.. doctest:: python
>>> list(prime_factors_gen(12))
[2, 3]
>>> list(prime_factors_gen(16))
[2]
"""
return (p for p in divisors_gen(n) if is_prime(p))
def prime_factors_gen(n):
"""prime factors generator
Args:
n (int): number to be factorized
Yields:
(int): prime factors w/o repeats
Examples:
>>> list(prime_factors_gen(12))
[2, 3]
>>> list(prime_factors_gen(16))
[2]
"""
return (p for p in divisors_gen(n) if is_prime(p))
def sum_divisors(n):
return sum(divisor for divisor in divisors_gen(n) if divisor < n)
def sum_proper_divisors(n):
return sum(divisors_gen(n)) - n
def proper_divisors_gen(n):
return sum(number for number in divisors_gen(n) if number < n)