# Find the number of reduced proper fractions
# where the denominator is less than 1000000
from useful import phi
tot = 0
for i in range(2, 1000001):
tot += phi(i)
print tot
# then (n^m) / phi(n^m) is constant for all m >= 1 from useful import PrimeList, phi primes = PrimeList(1000001) cands = set(range(2,1000001)) print "Ready!" for p in primes : temp = p while temp < 1000001 : cands.remove(temp) temp *= p for c in range(2,1001): temp = c temp *= c while temp < 1000001 : cands.discard(temp) temp *= c ma = 0 best = 0 for cand in reversed(list(cands)) : val = float(cand) / phi(cand) if val > ma : ma = val best = cand print best
