def we_are_done(count, n): numer = 99 denom = 100 g = gcd(n, count) count /= g n /= g return count == numer and n == denom
def phi(n):
i = 2
# Note, if n is prime, phi(n) = n-1
count = n-1
while i*i <= n:
if n % i == 0:
if gcd(i, n/i) == 1:
# If m and n are coprime, then phi(mn) == phi(m) * phi(n)
return PHI_VALUES[i] * PHI_VALUES[n/i]
else:
count -= 2 # The two divisors are removed from the count of co-prime ints less than n
i += 1
return count
def main():
min_ratio_so_far = sys.maxint
best_n = 1
# Build phi values for n <= approximately sqrt(10**7)
for n in range(1, NUM_PHI_VALS + 1):
PHI_VALUES[n] = phi(n)
for a in range(1, NUM_PHI_VALS + 1):
for b in range(a + 1, NUM_PHI_VALS + 1):
n = a*b
pn = PHI_VALUES[a] * PHI_VALUES[b]
if a*b <= 10**7 and gcd(a,b) == 1 and numbers_are_permutations(n, pn):
ratio = float(n) / (pn)
if ratio < min_ratio_so_far:
min_ratio_so_far = ratio
best_n = n
print "n = %d has the minimal ratio n/phi(n) for n <= 10**7" % (best_n)
