def generate_primes(start, end):
    primes = []
    for i in range(start, end):
        for j in range(2, i):
            if i % j == 0:
                break
        else:
            primes.append(i)
    return primes

def prime_factorization_with_help(x, primes, prime_factorization):
    prime_factorization = prime_factorization or {}
    for n in primes:
        if not x % n:
            prime_factorization[n] = prime_factorization.get(n, 0) + 1
            prime_factorization_with_help(x/n, primes, prime_factorization)
            break
    return prime_factorization

def number_of_factors_with_help(prime_factorization):
    answer = 1
    for prime, power in prime_factorization.items():
        answer *= power+1
    return answer

def better_composite_count(limit):
    answer = []
    primes = generate_primes(2, limit//2)
    most_divisors = 0
    for x in range(limit):
        _ = number_of_factors_with_help(prime_factorization_with_help(x+1, primes, []))
        if _ > most_divisors:
            most_divisors = _
            answer.append(x+1)
    return answer