def totient2(n):
try:
return d_totient[n]
except KeyError:
ret = n
if is_prime(n):
ret = n - 1
else:
fact = prime_factors(n)
for p in fact:
ret = ret*(p - 1)/p
k = 1
while True:
d_totient[n**k] = (n**(k - 1))*ret
k += 1
if n**k >= 10**6:
break
return d_totient[n]
def test0003(self):
from id_0003 import is_prime, prime_factors
primes = [2, 3, 5, 7, 11, 13, 17]
for x in primes:
self.assertEqual(is_prime(x), 1)
non_primes = [4, 6, 8, 10, 12, 14, 15, 16, 18]
for x in non_primes:
self.assertEqual(is_prime(x), 0)
self.assertEqual(prime_factors(2), [2])
self.assertEqual(prime_factors(3), [])
self.assertEqual(prime_factors(4), [2])
self.assertEqual(prime_factors(5), [])
self.assertEqual(prime_factors(6), [2, 3])
self.assertEqual(prime_factors(10), [2, 5])
self.assertEqual(prime_factors(13195), [5, 7, 13, 29])