Python programs to check if a number is a perfect number or not have been shown here. A perfect number is a positive integer that is equal to the sum of its proper divisors. For example 6 is a perfect number because if we add it's proper divisors (1, 2 and 3), we get 6 i.e. 1 + 2 + 3 = 6. Some of the other perfect numbers are 28, 496, 8128 etc.

## 1. Algorithm to check if a number is a perfect number or not

1. Take a number n as input.

2. Set s = 0, x = 1

3. Check if n is divisible by x

4. If step 3 is true perform s = s + x

5. Set x = x + 1

6. Go step 3 until x > n/2

7. If s = n declare "n is a perfect number"

## 2. Pseudocode to check if a number is a perfect number or not

Input : A positive number n

Output : n is a perfect number or not

1. Procedure isPerfectNumber(n):

2. s := 0

3. x := 1

4. Repeat until x > (n/2)

5. If n mod x = 0:

6. s := s + x

7. If n = s:

8. Return "Perfect number"

9. Else:

10. Return "Not a perfect number"

11. End Procedure

## 3. Time complexity to check if a number is a perfect number or not

Time Complexity: O(n)

n is the input number

## 4.1. Python Program & Output to check if a number is a perfect number or not using iteration

Code has been copied
##############################
#     alphabetacoder.com
# Python program to check if a
# number is a perfect number
##############################

# take input
n = int(input("Enter the number: "))

# initialize
s = 0

# add all the divisor upto n / 2
for i in range(1, (n // 2) + 1):
if n % i == 0:
s = s + i

# check if the input number
# is equal to the sum
if n == s:
print(n, "is a perfect number")
else:
print(n, "is not a perfect number")


Output

Case 1:

Enter the number: 6

6 is a perfect number

Case 2:

Enter the number: 50

50 is not a perfect number

Case 3:

Enter the number: 28

28 is a perfect number

## 4.2. Python Program & Output to check if a number is a perfect number or not using recursion

Code has been copied
#########################################
# 	    alphabetacoder.com
# Python program to check if a number is
# a perfect number using recursion
#########################################

# recursive function to check if input
# number is a perfect number or not
def isPerfect(n, i, s):
if i > (n // 2):  # exit condition
return s == n  # return true or false as per condition

if n % i == 0:  # check divisibility
s += i
# recursive call
return isPerfect(n, i + 1, s)

# main function
def main():
# take input
n = int(input("Enter the number: "))

# check if the input number is perfect
# by calling function
if isPerfect(n, 1, 0) == True:
print(n, "is a perfect number")
else:
print(n, "is not a perfect number")

# driver code
main()


Output

Enter the number: 496

496 is a perfect number