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p069.py
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p069.py
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def isprime(n):
'''check if integer n is a prime'''
# make sure n is a positive integer
n = abs(int(n))
# 0 and 1 are not primes
if n < 2:
return False
# 2 is the only even prime number
if n == 2:
return True
# all other even numbers are not primes
if not n & 1:
return False
# range starts with 3 and only needs to go up the squareroot of n
# for all odd numbers
for x in range(3, int(n**0.5)+1, 2):
if n % x == 0:
return False
return True
def primedivs(n):
"""returns a list of prime divisors of a number, containing [prime divisor, max exponent]"""
A = []
if isprime(n):
A.append([n, 1])
else:
for i in range (2, n/2 + 1):
if isprime(i) and n%i == 0:
exp = 0
aux = n
while aux%i == 0:
exp = exp + 1
aux = aux/i
A.append([i, exp])
return A
def totient(n):
res = 1
A = primedivs(n)
for i in range(0, len(A)):
if A[i][1] == 1:
res = res * (A[i][0] - 1)
else:
res = res * (A[i][0] - 1) * A[i][0]**(A[i][1] - 1)
return res
#print double(7)/double(totient(7))
n = 0
maximum = 0
for i in range(30030, 1000001, 30030):
x = double(i)/double(totient(i))
if x > maximum:
maximum = x
n = i
print n