Python program to check if a number is an amstrong number has been shown here. A positive integer of order n is called an amstrong number if the sum of each digit to the power n is equal to that number.

For example, 153 and 1634 are amstrong numbers as $153 = 1^3 + 5^3 + 3^3$ and $1634 = 1^4 + 6^4 + 3^4 + 4^4$.

The algorithm, pseudocode and time complexity of the program have been shown below.

## 1. Algorithm to check if a number is an amstrong number

1. Take input of a positive number n.

2. Calculate d, the total no of digit of n

3. Extract each digit $p_i$ and perform sum = $\sum_{i=1}^d p_i ^d$

4. Check If sum == n

5. If step 4 is true, then display n as an amstrong number

6. If step 4 is false, then display n as not an amstrong number

## 2. Pseudocode to check if a number is an amstrong number

Input : A postive number $n$ as input

Output : $n$ is an amstrong number or not an amstrong number

1. Procedure checkAmstrong($n$):

2. $t \leftarrow n$:

3. $sum \leftarrow 0$:

4. Count $d$, the total no of digits in $n$

5. Repeat until $t != 0$

6. $r \leftarrow t \mod 10$

7. $sum \leftarrow sum + r^d$

8. $t \leftarrow t / 10$

9. If $sum \mod n$ == 0:

10. Return "Amstrong number"

11. Else:

12. Return "Not an amstrong number"

13. End Procedure

## 3. Time complexity to check if a number is an amstrong number

Time Complexity: O(log(n))

Where log(n) is the total no of digits of the input number n.

## 4. Python Program & output to check if a number is an amstrong number

Code has been copied
# *************************************
#       alphabetacoder.com
# Python program to check if a number
# is an amstrong number or not
# *************************************

import math

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

# initialize
d = 0
t = n
s = 0
# calculate the number of digit
# in that number
while t != 0:
d += 1
t = t // 10

# copy value
t = n

# find the sum of digits each to the power d
while t != 0:
r = t % 10
s = s + math.pow(r, d)
t = t // 10

# check if input number is amstrong or not
if n == s:
print(n, "is an amstrong number!")
else:
print(n, "is not an amstrong number!")


Output

Enter the number = 1634

1634 is an amstrong number!