'''
Created on 2013-01-29
@author: paymahn
'''
'''
Use Eulers totient function:
http://www.math.okstate.edu/~wrightd/crypt/lecnotes/node18.html
'''
import CommonFunctions as cf
MAX = 10**6
totient = [0]*(MAX+1)
primes = cf.sieve_of_Erastothenes(MAX)
for i in range(2,MAX+1):
factors = cf.find_prime_factors(i, primes)
product = 1
for factor in factors:
product *= factor**factors[factor] - factor**(factors[factor]-1)
totient[i] = product
print sum(totient) * 3/7
Created on 2013-01-28
@author: paymahn
The idea is to make a sieve and cross of multiples.
All unique fractions are kept unmarked.
'''
import CommonFunctions as cf
from time import time
t = time()
MAX = 50
primes = set(cf.sieve_of_Erastothenes(MAX))
tally = 0
for denom in range(2,MAX + 1):
if denom in primes:
tally += denom - 1
else:
if denom %2 == 0:
jump = 2
else:
jump = 1
for num in range(1,denom,jump):
if cf.gcd(num, denom) == 1:
tally += 1
import CommonFunctions as cf
sieve = cf.sieve_of_Erastothenes(10000)
best_num = 0
best_ratio = 0
for i in range(1,1000000):
phi = cf.eulers_totient(i, sieve=sieve)
if i / phi > best_ratio:
best_ratio = i / phi
best_num = i
print best_num
