g = {1:False,2:True}
def is_prime(n):
    if n in g:
        return g[n]
    g[n] = all(n%k>0 for k in range(2,n))
    return g[n]
def perfect_numbers(n: int) -> list[int]:
    rest = []
    for z in range(1,n+1):
        if is_prime(z):
            z = (2**z-1)*(2**(z-1))
            if n>=z:
                rest.append(z)
    return rest