**Zumkeller numbers** are the set of numbers whose divisors can be partitioned into two disjoint sets that sum to the same value. The first few zumkeller numbers are **6, 12, 20, 24, 28, 30, 40, 42, 48, 54, …**.

In this article, we will find the N^{th} Zumkeller number.

**Find the N ^{th} Zumkeller Number:** Given a number

**N**, the task is to find the N

^{th}Zumkeller number.

**Examples:**

Input:N = 2

Output:12

Explanation:

The second Zumkeller number is 12.

Input:N = 5

Output:28

**Approach:** The following steps are followed to compute the answer.

- Get the number N.
- Iterate over the loop starting from i = 1 until Nth Zumkeller number is found.
- Check the number ‘i’ is a zumkeller number or not.
- If yes, then repeat the above step for i+1 and increment the counter.
- If no, then repeat the above step for i+1 without incrementing the counter.
- Finally, when the counter is equal to the number N, that number is the N-th zumkeller number. Print the value of ‘i’ and break the loop.

Below is the implementation of the above approach:

## Python3

`# Python program to find the ` `# N-th Zumkeller number ` ` ` `# Function to find all the ` `# divisiors ` `def` `Divisors(n) : ` ` ` `l ` `=` `[] ` ` ` `i ` `=` `1` ` ` `while` `i <` `=` `n : ` ` ` `if` `(n ` `%` `i ` `=` `=` `0` `) : ` ` ` `l.append(i) ` ` ` `i ` `=` `i ` `+` `1` ` ` `return` `l ` ` ` `# Function to check if the sum ` `# of the subset of divisors is ` `# equal to sum / 2 or not ` `def` `PowerSet(arr, n, s): ` ` ` ` ` `# List to find all the ` ` ` `# subsets of the given set. ` ` ` `# Any repeated subset is ` ` ` `# considered only ` ` ` `# once in the output ` ` ` `_list ` `=` `[] ` ` ` ` ` `# Run a counter i ` ` ` `for` `i ` `in` `range` `(` `2` `*` `*` `n): ` ` ` `subset ` `=` `"" ` ` ` ` ` `# Consider each element ` ` ` `# in the set ` ` ` `for` `j ` `in` `range` `(n): ` ` ` ` ` `# Check if j-th bit in ` ` ` `# the i is set. ` ` ` `# If the bit is set, ` ` ` `# we consider ` ` ` `# j-th element from set ` ` ` `if` `(i & (` `1` `<< j)) !` `=` `0` `: ` ` ` `subset ` `+` `=` `str` `(arr[j]) ` `+` `"|"` ` ` ` ` `# Check if the subset is ` ` ` `# encountered for the first time. ` ` ` `if` `subset ` `not` `in` `_list ` `and` `len` `(subset) > ` `0` `: ` ` ` `_list.append(subset) ` ` ` ` ` `# Consider every subset ` ` ` `for` `subset ` `in` `_list: ` ` ` `sum` `=` `0` ` ` ` ` `# Split the subset and ` ` ` `# sum of its elements ` ` ` `arr ` `=` `subset.split(` `'|'` `) ` ` ` `for` `string ` `in` `arr[:` `-` `1` `]: ` ` ` `sum` `+` `=` `int` `(string) ` ` ` ` ` `# If the sum is equal ` ` ` `# to S ` ` ` `if` `sum` `=` `=` `s: ` ` ` `return` `True` ` ` ` ` `return` `False` ` ` `# Function to check if a number ` `# is a Zumkeller number ` `def` `isZumkeller(n): ` ` ` ` ` `# To find all the divisors ` ` ` `# of a number N ` ` ` `d ` `=` `Divisors(n) ` ` ` ` ` `# Finding the sum of ` ` ` `# all the divisors ` ` ` `s ` `=` `sum` `(d) ` ` ` ` ` `# Check for the condition that ` ` ` `# sum must be even and the ` ` ` `# maximum divisor is less than ` ` ` `# or equal to sum / 2. ` ` ` `# If the sum is odd and the ` ` ` `# maximum divisor is greater than ` ` ` `# sum / 2, then it is not possible ` ` ` `# to divide the divisors into ` ` ` `# two sets ` ` ` `if` `not` `s ` `%` `2` `and` `max` `(d) <` `=` `s ` `/` `2` `: ` ` ` ` ` `# For all the subsets of ` ` ` `# the divisors ` ` ` `if` `PowerSet(d, ` `len` `(d), s ` `/` `2` `) : ` ` ` `return` `True` ` ` ` ` `return` `False` ` ` ` ` `# Function to print N-th ` `# Zumkeller number ` `def` `printZumkellers(N): ` ` ` `val ` `=` `0` ` ` `ans ` `=` `0` ` ` ` ` `# Iterating through all ` ` ` `# the numbers ` ` ` `for` `n ` `in` `range` `(` `1` `, ` `10` `*` `*` `5` `): ` ` ` ` ` `# Check if n is a ` ` ` `# Zumkeller number ` ` ` `if` `isZumkeller(n): ` ` ` `ans ` `=` `n ` ` ` `val ` `+` `=` `1` ` ` ` ` `# Check if N-th Zumkeller number ` ` ` `# is obtained or not ` ` ` `if` `val >` `=` `N: ` ` ` `break` ` ` ` ` `print` `(ans) ` ` ` `# Driver code ` `if` `__name__ ` `=` `=` `'__main__'` `: ` ` ` ` ` `N ` `=` `4` ` ` ` ` `printZumkellers(N) ` |

*chevron_right*

*filter_none*

**Output:**

24

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