Python program to print all Disarium numbers between 1 to 100

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, 89 is a Disarium number because 8¹ + 9² = 8 + 81 = 89.

To find all Disarium numbers between 1 and 100, we need to calculate the length of each number and check if the sum of digits raised to their positional powers equals the original number.

Complete Program

def length_calculation(my_val):
    len_val = 0
    while(my_val != 0):
        len_val = len_val + 1
        my_val = my_val//10
    return len_val

def digit_sum(my_num):
    remaining = sum_val = 0
    len_fun = length_calculation(my_num)
    while(my_num > 0):
        remaining = my_num%10
        sum_val = sum_val + (remaining**len_fun)
        my_num = my_num//10
        len_fun = len_fun - 1
    return sum_val

ini_result = 0
print("The disarium numbers between 1 and 100 are:")
for i in range(1, 101):
    ini_result = digit_sum(i)
    if(ini_result == i):
        print(i)

The disarium numbers between 1 and 100 are:
1
2
3
4
5
6
7
8
9
89

How It Works

The program uses two helper functions:

• length_calculation() ? Counts the number of digits in a given number
• digit_sum() ? Calculates the sum of digits raised to their respective positional powers

Step-by-Step Process

For each number from 1 to 100:

1. Calculate the total number of digits
2. Extract each digit from right to left
3. Raise each digit to the power of its position (starting from the leftmost position)
4. Sum all these powered values
5. Compare with the original number

Example Verification

Let's verify why 89 is a Disarium number ?

number = 89
print(f"Checking {number}:")
print(f"8^1 + 9^2 = {8**1} + {9**2} = {8**1 + 9**2}")
print(f"Is {number} a Disarium number? {8**1 + 9**2 == number}")

Checking 89:
8^1 + 9^2 = 8 + 81 = 89
Is 89 a Disarium number? True

Conclusion

Disarium numbers between 1 and 100 are mostly single digits (1-9) and one two-digit number (89). The algorithm systematically checks each number by calculating the sum of digits raised to their positional powers.