Check if a number is a Krishnamurthy Number or not in PYTHON

By Kalki Pareshkumar Bhavsar

A Python implementation to check whether the input number is a Krishnamurthy number (a number that is equal to the sum of the factorial of each of its digits) or not. 

Krishnamurthy Number

Hey CodeSpeeder!

Numbers are amazing when it comes to finding patterns within the number themselves. 

Consider a number, for example, 145. There are a total of 3 digits in the number: 1, 4, and 5 whose factorial is 1, 24, and 120 respectively. Add them up and you'll get 145, the input number again. Isn't this fascinating! Such numbers are specially named as Krishnamurthy number, Strong number, or Peterson number. 

Let's mathematically formulate this! Consider a number num with n digits be expressed as d_nd_n-1...d₁. num is a Krishnamurthy number if the following condition is satisfied:

d_nd_n-1...d₁ = d_n! + d_n-1! +...+ d₁!

For example:

Number 145 is a 3-digit number. From the above condition, LHS=145 while RHS = 1! + 5! +4! = 145 = LHS. 145 is a Krishnamurthy number.

Number 154 is also a 3-digit number. Here, LHS=154 while RHS = 1! + 5! +4!  = 145. Hence, 154 is not a Krishnamurthy number.

Program

The following is the Python implementation for checking whether the input number is a Krishnamurthy number or not:

import math

# function to check if the number n
# is Krishnamurthy number or not
def isKrishnamurthyNumber(num):
    sumVal = 0  # Sum value
    # calculate the sum of the factorial of each digit in number num
    for digit in str(num):
        sumVal += math.factorial(int(digit))

    # if the sumVal is equal to input number num,
    # num is an Krishnamurthy number
    if sumVal == num:
        return True
    else:
        return False

Test-cases and Output

The below is the driver code to check the function isKrishnamurthyNumber() on various test-cases:

# Test-case 1: 1 is a Krishnamurthy number
print("Is 1 a Krishnamurthy Number? - ", isKrishnamurthyNumber(1))
# Test-case 2: 2is not a Krishnamurthy number
print("Is 2 a Krishnamurthy Number? - ", isKrishnamurthyNumber(2))
# Test-case 3: 145 is a Krishnamurthy number
print("Is 145 a Krishnamurthy Number? - ", isKrishnamurthyNumber(145))
# Test-case 4: 154 is not a Krishnamurthy number
print("Is 154 a Krishnamurthy Number? - ", isKrishnamurthyNumber(154))
# Test-case 5: 40585 is a Krishnamurthy number
print("Is 40585 a Krishnamurthy Number? - ", isKrishnamurthyNumber(40585))

 

The output of the following code is:

Is 1 a Krishnamurthy Number? -  True
Is 2 a Krishnamurthy Number? -  True
Is 145 a Krishnamurthy Number? -  True
Is 154 a Krishnamurthy Number? -  False
Is 40585 a Krishnamurthy Number? -  True

 

Fact point! 

There are exactly four Krishnamurthy numbers which are 1, 2, 145, and 40585 at present known.