def solve(D):
primes = sieve_eratosthenes(D)
factorizations = list(factorizations_below(D, primes))
assert len(factorizations)+1 == D
return sum([phi_of_factorization(factorization) for factorization in factorizations])
def solve(D, i):
primes = sieve_eratosthenes(D)
l = list(factorizations_below(D, primes)) + [((1,1),)]
E = sorted([(num(factors), rad(factors)) for factors in l], cmp_rad)
return E[i-1][0]