Checking for Smith Number in Python using Functions

In this Python tutorial, we will learn about Smith Numbers and how to generate them in Python.

What are Smith Numbers?

Smith numbers have the following features:-

• They are composite numbers
• Sum of its digits is equal to the summation of the sum of the digits of its prime factors.

Let’s look at a few examples of Smith Numbers to understand the same:-

1. 85. The sum of its digits is 8+5 = 13. Its prime factors are 5 and 17. Sum of the digits of prime factors are 5 + (1+7)= 13. Hence 85 is a Smith Number.
2. 27. The sum of its digits is 2+7=9. Its prime factors are 3,3 and 3 Sum of the digits of prime factors are 3 + 3 + 3= 9. Hence 27 is a Smith Number

Let us now look at the Code in Python…

Code and Output

Code in Python:-

#Function to calculate the number of digits in a number
def digCount(num):
    c = 0
    while num != 0:
        num = num//10
        c += 1
    return c
#Function to calculate the sum of digits of a number
def digSum(num):
    temp = num
    sum = 0
    for i in range(digCount(num)):
        sum+=num%10
        num//=10
    return sum
#Function to check whether a number is prime or not
def isPrime(num):
    for i in range(2,num):  
       if (num % i) == 0:  
           return False
       else:  
           continue
    return True
           
          
 #Function to check whether a number is a Smith Number or not      
def isSmith(num):
    if(isPrime(num)):
         print("This is a prime number and only composite numbers can be Smith numbers")
    else:
        prime_factors = []
        temp = num
        c = 2
        while(temp>1):
            if(temp%c == 0 and isPrime(c)):
                prime_factors.append(c)
                temp/=c
            else:
                c+=1
                continue
        for i in range(0,len(prime_factors)):
            if(digCount(prime_factors[i])>1):
                while(digCount(prime_factors[i])>1):
                    prime_factors[i] = digSum(prime_factors[i])
        if(sum(prime_factors) == digSum(num)):
            return True
        else:
            return False
#Checking a list of numbers whether they are Smith Numbers or not       
list = [25,27,83,85,90,94,120,121,200,202]
for num in list:
    if(isSmith(num)):
        print(f'{num} is a Smith Number')
    else:
        print(f'{num} is not a Smith Number')

Run this program online

Output:-

25 is not a Smith Number
27 is a Smith Number
This is a prime number and only composite numbers can be Smith numbers
83 is not a Smith Number
85 is a Smith Number
90 is not a Smith Number
94 is not a Smith Number
120 is not a Smith Number
121 is a Smith Number
200 is not a Smith Number
202 is a Smith Number

Please try and understand the code using pen and paper before moving on to the explanation of the Python code below!

Explanation of the code

Let us look at what the functions are supposed to do in this code:-

1. digCount() function: Counts the number of digits of the argument passed to it and returns it.
2. digSum() function: Returns the sum of digits of the argument passed to it.
3. isPrime() function: Checks, whether the argument passed, is a prime number or not.

We iterate over a list of numbers and pass them on to the isSmith() function.

The function firsts checks whether the argument passed is a prime number or not. If the argument is a prime number then we print “This is a prime number and only composite numbers can be Smith numbers”.

If the argument is not a prime number, then we find out the prime factors of the argument passed and append it to the list prime_factors.

After having the prime factors of the argument passed, we iterate over the list prime_factors and calculate the sum of digits of every prime factor, replacing them with the sum of their respective digits.

Then we consider the sum of all the elements of the prime_factors list (which now contains the sum of digits of prime factors) and check whether it is equal to the sum of digits of the argument passed. If those two are equal, then the argument passed is a Smith Number and the function returns True. Otherwise, the function returns False because the argument is not a Smith Number.

I hope this Python tutorial was useful for you!