Print all perfect numbers less than N

Question

I am trying to print all perfect numbers lesser than an integer, but I am not sure how to do it. Could you help me, please? When I execute the code, it writes ValueError: invalid literal for int() with base 10 .

My code:

n = input() 
w = int(n) - 1
i = 0
a = 0
z = 0
list = []
for w in range(w, 1):
    for i in range(w, 2):
        if w % i == 0:
            a = int(w / i)
            z = z + a
    if z == w:
        list.append(w)
print(list)

What is a perfect number?

In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself.

Answer 1

Here's how you can do it:

n = input('Enter the integer:') 
w = int(n) - 1
l = [] # creating an empty list 'l'
for i in range(w, 0, -1): # Runs the loop for all integers below n and greater than 0. 
  s = 0 # Set the sum to 0. 
  for j in range(i,0, -1): # Runs the loop till 0 to check for all divisors
    if i % j == 0 and j!= i: # If the number is a divisor of 'i' and not equal to the 'i' itself. 
      s = s + j # Then add the divisor to the sum
  if s == i: # If sum is equal to the number 'i'
    l.append(i) # Then add the number 'i' to the list 'l'
print(l)

Output:

Enter the integer:10000
[8128, 496, 28, 6]

What you were doing wrong?

1. Naming a list by a Python keyword is a bad practice and should be avoided! You named the list by the name list which is a keyword in Python.
2. You were using the same variable names for different tasks such as w for denoting integer less than n and also range in for loop. This should be avoided too!
3. Idk, why you were using the variable a but there's no need to initialize variables with 0 if you are using as range in for loop .
4. You were running the for loop till 1 instead should run it 0 .
5. You were not setting the sum to zero at every integer.

Answer 2

Here is a very simple implementation of the perfect numbers algorithm:

def isperfect(n: int) -> bool:
    """Test if a number is perfect."""
    sum_ = sum(i for i in range(1, n//2+1) if not n % i)
    return sum_ == n

n = int(input('Enter a positive integer: '))
p = [i for i in range(1, n) if isperfect(i)]

Output:

Enter a positive integer: 10000

print('Perfect numbers:', *p)
Perfect numbers:  6 28 496 8128

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Explanation:

1. The isperfect function is used to test whether n is perfect. Efficiency is gained by only testing numbers <= n/2.
2. Capture the user's requested integer.
3. Using list comprehension, iterate the range of values (N-1) and test if each is perfect.
4. The perfect numbers are captured and stored into the p variable as a list .