求Zumkeller数的第N个项

Zumkeller数字是其除数可以划分为两个不相交的集合的总和，这些集合的总和等于相同的值。前几个Zumkeller编号是6、12、20、24、28、30、40、42、48、54 … 。

在本文中，我们将找到第N^个Zumkeller编号。

查找第N^个Zumkeller编号：给定数字N ，任务是找到第N^个Zumkeller编号。

例子：

Input: N = 2
Output: 12
Explanation:
The second Zumkeller number is 12.

Input: N = 5
Output: 28

方法：按照以下步骤计算答案。

1. 获取数字N。
2. 从i = 1开始循环遍历，直到找到第N个Zumkeller编号。
3. 检查数字“ i”是否为zumkeller数字。
4. 如果是，则对i + 1重复上述步骤并增加计数器。
5. 如果否，则对i + 1重复上述步骤，而无需增加计数器。
6. 最后，当计数器等于数字N时，该数字即为第N个祖克梅勒数字。打印’i’的值并中断循环。

下面是上述方法的实现：

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)

输出：

24