def get_lcm(l):
factor_lists = [get_prime_factors(e) for e in l]
factors = get_factor_set(factor_lists)
d = defaultdict(int)
for factor in factors:
for fl in factor_lists:
if fl.count(factor) > d[factor]:
d[factor] = fl.count(factor)
return product([k**v for k,v in d.items()])
def main():
target = 4
candidate = 0
consecutive_successes = 0
while consecutive_successes < target:
candidate += 1
if len(set(get_prime_factors(candidate))) == target:
consecutive_successes += 1
else:
consecutive_successes = 0
print(candidate - 3)
def get_num_factors(n):
# very slow but works ¯\_(ツ)_/¯
factors = get_prime_factors(n)
num_facs = len(factors)
for prim in factors:
fac = prim * 2
while fac <= n**(1 / 2):
if n % fac == 0 and fac not in factors:
num_facs += 1
factors.append(fac)
fac += prim
return num_facs, factors
def run():
"""
Solution: Brute force
"""
first, consec = 0, 0
n = 647
while consec < 4:
factors = get_prime_factors(n)
if len(factors) == 4:
if consec == 0:
first = n
consec += 1
else:
consec = 0
first = 0
n += 1
return first
def main():
print(get_prime_factors(600851475143)[-1])
def euler_totient(n):
ret = n
for p in set(get_prime_factors(n)):
ret //= p
ret *= p - 1
return ret
def divisors(n):
prime_factors = get_prime_factors(n)
s = set(prime_factors)
l = [prime_factors.count(e) for e in s]
lx = [e + 1 for e in l]
return product(lx)
def count_factors(n):
prime_factors = Counter(get_prime_factors(n))
total_factors = 1
for prime, multiplicity in prime_factors.items():
total_factors *= multiplicity + 1
return total_factors
def get_prime_factor_tuples(n):
d = defaultdict(int)
for e in get_prime_factors(n):
d[e] += 1
return sorted(d.items(), key=lambda e: e[0])
from utils import get_prime_factors
if __name__ == "__main__":
print max(get_prime_factors(600851475143))
def solve():
number = 600851475143
primes = get_prime_factors(number)
answer = max(primes)
print(answer)
import numpy as np from utils import prime_numbers, get_prime_factors n = 600851475143 prime_list = prime_numbers(int(np.sqrt(n) + 1)) print(np.max(get_prime_factors(n, prime_list)))
def test_get_prime_factors():
assert utils.get_prime_factors(60) == [2, 2, 3, 5]
assert utils.get_prime_factors(73) == [73]
assert utils.get_prime_factors(1) == []