Perfect Number formula in Python Question an Mersenne Numbers

[Pleiades]

see: https://www.w3resource.com/python-exerci...ise-11.php

Thanks Larz60,

Now I'm trying to write code for a simple formula 4**y*2-1=
Input y several times with different numbers automated. I believe I need some kinda of exponent loop so I can integrate it with the Perfect Numbers module, but I'm clueless. Plz help.

For you perfect Number people here is the ultimate code:

from itertools import count

def postponed_sieve():                   # postponed sieve, by Will Ness      
    yield 2; yield 3; yield 5; yield 7;  # original code David Eppstein, 
    sieve = {}                           #   Alex Martelli, ActiveState Recipe 2002
    ps = postponed_sieve()               # a separate base Primes Supply:
    p = next(ps) and next(ps)            # (3) a Prime to add to dict
    q = p*p                              # (9) its sQuare 
    for c in count(9,2):                 # the Candidate
        if c in sieve:               # c's a multiple of some base prime
            s = sieve.pop(c)         #     i.e. a composite ; or
        elif c < q:  
             yield c                 # a prime
             continue              
        else:   # (c==q):            # or the next base prime's square:
            s=count(q+2*p,2*p)       #    (9+6, by 6 : 15,21,27,33,...)
            p=next(ps)               #    (5)
            q=p*p                    #    (25)
        for m in s:                  # the next multiple 
            if m not in sieve:       # no duplicates
                break
        sieve[m] = s                 # original test entry: ideone.com/WFv4f

def prime_sieve():                   # postponed sieve, by Will Ness      
    yield 2; yield 3; yield 5; yield 7;  # original code David Eppstein, 
    sieve = {}                           #   Alex Martelli, ActiveState Recipe 2002
    ps = postponed_sieve()               # a separate base Primes Supply:
    p = next(ps) and next(ps)            # (3) a Prime to add to dict
    q = p*p                              # (9) its sQuare 
    for c in count(9,2):                 # the Candidate
        if c in sieve:               # c’s a multiple of some base prime
            s = sieve.pop(c)         #     i.e. a composite ; or
        elif c < q:  
             yield c                 # a prime
             continue              
        else:   # (c==q):            # or the next base prime’s square:
            s=count(q+2*p,2*p)       #    (9+6, by 6 : 15,21,27,33,...)
            p=next(ps)               #    (5)
            q=p*p                    #    (25)
        for m in s:                  # the next multiple 
            if m not in sieve:       # no duplicates
                break
        sieve[m] = s                 # original test entry: ideone.com/WFv4f

def mod_mersenne(n, prime, mersenne_prime):
    while n > mersenne_prime:
        n = (n & mersenne_prime) + (n >> prime)
    if n == mersenne_prime:
        return 0
    return n

def is_mersenne_prime(prime, mersenne_prime):
    s = 4
    for i in range(prime - 2):
        s = mod_mersenne((s*s - 2), prime, mersenne_prime)
    return s == 0

def calculate_perfects():
    yield(6)
    primes = prime_sieve()
    next(primes)                     #2 is barely even a prime
    for prime in primes:
        if is_mersenne_prime(prime, 2**prime-1):
            yield(2**(2*prime-1)-2**(prime-1))

if __name__ == '__main__':
    for perfect in calculate_perfects():
        print(perfect)