Python program to check if the given number is a Disarium Number

A Disarium Number is a number where the sum of its digits raised to the power of their respective positions equals the original number itself. For example, 175 is a Disarium number because 1¹ + 7² + 5³ = 1 + 49 + 125 = 175.

Understanding Disarium Numbers

To check if a number is a Disarium number, we need to ?

• Extract each digit from the number
• Calculate the total number of digits
• Raise each digit to the power of its position (1-based indexing)
• Sum all the results and compare with the original number

Method 1: Using Helper Function

This approach uses a separate function to calculate the number of digits ?

def length_calculation(num_val):
    length = 0
    while(num_val != 0):
        length = length + 1
        num_val = num_val//10
    return length

my_num = 175
remaining = sum_val = 0
len_val = length_calculation(my_num)

print("Original number:", my_num)
num_val = my_num

while(my_num > 0):
    remaining = my_num % 10
    sum_val = sum_val + int(remaining**len_val)
    my_num = my_num // 10
    len_val = len_val - 1

if(sum_val == num_val):
    print(str(num_val) + " is a disarium number!")
else:
    print(str(num_val) + " isn't a disarium number")

Original number: 175
175 is a disarium number!

Method 2: Using String Conversion

A simpler approach using string methods to extract digits ?

def is_disarium(number):
    num_str = str(number)
    total = 0
    
    for i, digit in enumerate(num_str):
        total += int(digit) ** (i + 1)
    
    return total == number

# Test with different numbers
test_numbers = [175, 192, 518, 135]

for num in test_numbers:
    if is_disarium(num):
        print(f"{num} is a disarium number!")
    else:
        print(f"{num} is not a disarium number")

175 is a disarium number!
192 is not a disarium number
518 is a disarium number!
135 is a disarium number!

Step-by-Step Verification

Let's verify 175 step by step ?

number = 175
digits = [int(d) for d in str(number)]
print(f"Number: {number}")
print(f"Digits: {digits}")

total = 0
for i, digit in enumerate(digits, 1):
    power_result = digit ** i
    total += power_result
    print(f"{digit}^{i} = {power_result}")

print(f"Sum: {total}")
print(f"Is Disarium: {total == number}")

Number: 175
Digits: [1, 7, 5]
1^1 = 1
7^2 = 49
5^3 = 125
Sum: 175
Is Disarium: True

Comparison of Methods

Conclusion

A Disarium number has the sum of its digits raised to their positional powers equal to the original number. The string conversion method is more readable, while the mathematical approach is slightly more efficient for large numbers.