Perfect numbers

A proper divisor of a number is a positive factor of that number other than the number itself. For example, the proper divisors of 6 are 1, 2, and 3. A perfect number is a positive integer that is equal to the sum of its proper positive divisors. For instance, $6 = 1 + 2 + 3$ and $28 = 1 + 2 + 4 + 7 + 14$ are perfect numbers. In contrast, $1, 2, 3$ and $18$ are not perfect.

Write a function @show_perfect(f)@ that given a list $f$ of integers greater than zero computes the first perfect number that appears in $f$ , if any. When $f$ has no perfect numbers the function returns $-1$ .

The following function @proper_divisors(n)@ that computes the ordered list of proper divisors of a natural number $n$ can be helpful.

def proper_divisors(n):
    '''
    n is an integer greater than zero
    returns the ordered list of proper divsisors of n
    >>> proper_divisors(6)
    [1, 2, 3]
    >>> proper_divisors(284)
    [1, 2, 4, 71, 142]
    >>> proper_divisors(1)
    []
    '''
    if n == 1:
        return []
    result = [1]
    d = 2
    while d*d <= n:
        if n%d == 0:
            result.append(d)
            if n//d != d:
                result.append(n//d)
        d += 1
    return sorted(result)

Sample session

Problem information

Author: ProAl

Generation: 2026-01-25T17:19:36.450Z