Question

A proper divisor of a positive integer $n$ is a positive integer $d < n$ such that $d$ divides $n$ evenly, or alternatively if $n$ is a multiple of $d$. For example, the proper divisors of 12 are 1, 2, 3, 4, and 6, but not 12. A positive integer $n$ is called double-perfect if the sum of its proper divisors equals $2n$. For example, 120 is double-perfect (and in fact is the smallest double-perfect number) because its proper divisors are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, and 60, and their sum is 240, which is twice 120. There is only one other 3-digit double-perfect number. Write a Python program to find it, and enter the number as your answer below.

Answer 1

Answer:

The program written in Python is as follows:

See Explanation section for line by line explanation

for n in range(100,1000):

     isum = 0

     for d in range(1,n):

           if n%d == 0:

                 isum += d

     if isum == n * 2:

           print(n)

Explanation:

The program only considers 3 digit numbers. hence the range of n is from 100 to 999

for n in range(100,1000):

This line initializes sum to 0

     isum = 0

This line is an iteration that stands as the divisor

     for d in range(1,n):

This line checks if a number, d can evenly divide n

           if n%d == 0:

If yes, the sum is updated

                 isum += d

This line checks if the current number n is a double-perfect number

     if isum == n * 2:

If yes, n is printed

           print(n)

When the program is run, the displayed output is 120 and 672