def p073(N=12000):
retval = 0
for d in range(2,N+1):
total = p069.phi(d)
lowerthird = len([n for n in range(d/3+1) if numty.gcd(n,d) == 1])
retval += total/2-lowerthird
return retval
def p072(N=10**6):
table = numty.factortable(N + 1)
return sum(p069.phi(n, table[n]) for n in range(2, N + 1))
def p072(N=10**6):
table = numty.factortable(N+1)
return sum(p069.phi(n, table[n]) for n in range(2,N+1))
