def num_divisors(n):
f = factor(n)
count = 0
val = 0
prod = 1
for p in f:
if p != val:
prod *= count + 1
count = 0
val = p
count += 1
prod *= count + 1
return prod
def totient(n):
f = list(factor(n))
prod = 1
for p in f:
prod *= (1 - float(1) / p)
return int(round(prod * n))
def c_n(n): return sum(factor(n).keys())
from helpers import factor, cached_prime
limit = 1000000
cached_prime(limit)
c0 = len(factor(6))
c1 = len(factor(7))
c2 = len(factor(8))
c3 = len(factor(9))
for i in range(10, limit):
c0 = c1
c1 = c2
c2 = c3
c3 = len(factor(i))
if c0 == 4 and c1 ==4 and c3 == 4 and c2 == 4:
print i-3
""" Problem 3: Largest prime factor The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143? """ from helpers import factor print(factor(600851475143))