from eulerlib import cmpf, gcd N = 12000 f1 = (1,3) f2 = (1,2) c = 0 for d in xrange(1,N+1): for n in xrange(d/3,d/2+1): if gcd(n,d) == 1: f = (n,d) if cmpf(f,f1) > 0 and cmpf(f,f2) < 0: c += 1 print c
while n <= N:
m = n
s = 0
while m % p == 0:
s += 1
m /= p
prime_factors[n].append((p, s))
n += p
#calculate Euler Phi function
for p in all_primes:
n = p
prev = phi[1]
while n <= N:
phi[n] = n - n / p
prev = n
n *= p
def euler_phi(n):
if phi[n] < 0:
phi[n] = 1
for f in prime_factors[n]:
phi[n] *= phi[f[0]**f[1]]
return phi[n]
ratios = [(n, euler_phi(n)) for n in xrange(1, N + 1)]
print reduce(lambda r1, r2: r1 if cmpf(r1, r2) > 0 else r2, ratios)[0]
n = p while n <= N: m = n s = 0 while m % p == 0: s += 1 m /= p prime_factors[n].append((p,s)) n += p #calculate Euler Phi function for p in all_primes: n = p prev = phi[1] while n <= N: phi[n] = n - n/p prev = n n *= p def euler_phi(n): if phi[n] < 0: phi[n] = 1 for f in prime_factors[n]: phi[n] *= phi[f[0]**f[1]] return phi[n] ratios = [(n,euler_phi(n)) for n in xrange(1,N+1)] print reduce(lambda r1, r2: r1 if cmpf(r1,r2) > 0 else r2, ratios)[0]