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))