Perfect numbers

[Vidar567]

Gentlemans, do you have any suggestions why this code doesn't output proper values?

When I write end = 100 it outputs:
[6, 24, 28]

24 is not a perfect number.

def perfect_number(end = 100):

    lista = []
    for n in range(2, end):
        sum = 0
        for x in range(1, n):
            if n % x == 0:
                sum += x
            if sum == n:
                lista.append(n)
                sum = 0
    return lista
print(perfect_number())

[bowlofred]

You should be checking if after you get *all* the factors of a number, that they sum to that number. But that's not what your code does.

Your code is checking the sum after every number check (even the ones that aren't factors). If the sum to that point is equal to the number, then you add it.

In the case of 24, the factors are:
1, 2, 3, 4, 6, 8 => sums to 24, you declare a match...
Oops, 12 is also a factor. Sum is now 36, but it's too late. It's already added.

Basically, you shouldn't be looking at the sum inside the inner loop.

[Vidar567]

That's true I find it just seconds before:

"The if (sum == n) check needs to be done outside the loop. Otherwise you might pick up numbers such that the sum of a subset of divisors equals the number.

In fact, 24 is one such example since 1+2+3+4+6+8=24. Your code prematurely concludes that 24 is perfect, despite it also being divisible by 12."

This is good:

def perfect_number(end = 9001):

    lista = []
    for n in range(2, end+1):
        sum = 0
        for x in range(1, n):
            if n % x == 0:
                sum = sum + x
        if sum == n:
            lista.append(n)
            
    return lista
print(perfect_number())