def METHOD_NAME(level):
    # returns level_radical, level_primes, level_is_prime, level_is_prime_power, level_is_squarefree, level_is_square
    fact = Integer(level).factor()
    level_primes = [elt[0] for elt in fact]
    level_radical = prod(level_primes)
    level_is_prime_power = len(fact) == 1
    level_is_prime = level_is_prime_power and level_radical == level
    level_is_square = all( elt[1] % 2 == 0 for elt in fact)
    level_is_squarefree = all( elt[1] == 1 for elt in fact)
    return [level_radical, level_primes, level_is_prime, level_is_prime_power, level_is_squarefree, level_is_square]