Untouchable Number in Java

If a number N cannot be divided properly by any positive number, it is said to be an untouchable number. Additionally known as nonaliquot numbers. The sequence is A005114 from the OEIS.

It is a positive integer that cannot be represented as the sum of any positive integer's suitable divisors, unlike the untouchable number.

Properties

•  A number that cannot be divided is not a perfect number.
• All untouchable numbers are composite, with the exception of 2 and 5.

It is not an impossible number since the number 4 equals the total of the proper divisors of the number 9, i.e., 1+3 = 4.

Because it is not equal to the appropriate sum of any positive integer's divisors, the number 5 is untouchable. The only method to write 5 is as 1+4 in other words (there are no other ways). A number is equally divided by the digits 4 and 2. As a result, it is impossible to add 1+4 to any legitimate divisor.

The only odd untouchable number, as far as we can tell, is 5.

Steps to Solve an Untouchable Number

1. Declare a number X.
2. Find all the divisors of the given number X.
3.  Verify whether the number x is untouchable if the sum of all its proper divisors equals x, or whether it is not.
4. Check if i is the divisor of X or not:
   • If yes, add x to the variable a.
   • Else, add sum, x (divisor), and the resultant of (a/x) together.
   • At last, add 1 to the variable a.

Example:

The number 4 is not untouchable just because it is equal to the sum of the proper divisors of the number 9, for example, 1 + 3. The number 5 is untouchable because it does not equal the sum of the proper divisors of any positive integer.The only way to express 5 as the sum of distinct positive integers up to and including 1 is to write it as 5 = 1 + 4, but since 2 also divides by 4, it is impossible for 1 + 4 to equal the sum of all of a number's legitimate divisors (since the list of factors would have to contain both 4 and 2).

// java program to demonstrate untouchable number
import java.util.Scanner;  
public class solution
{  
//function determines the supplied number is an untouchable number or not.
static booleanisUntouchable(int x)  
{  
for(int n = 1; n<= 2 * x; n++)  
{  
if (sumOfDivisors(n) == x)  
return false;  
}  
return true;  
}    
static int sumOfDivisors(int a)  
{  
//stores the sum of the divisors  
int a = 0;  
//finds all the divisors of the number  
for(int n = 2; n<= Math.sqrt(a); n++)  
{  
// n is divisor of num  
if (a % n == 0)  
{  
//if equal, add only once, else add both  
if (n == (a / n))  
a = a + n;  
else  
a = a + (n + a / n);  
}  
}  
//1 is added to the variable sum because 1 is also a divisor  
return (a + 1);  
}  
//driver code  
public static void main(String args[])  
{  
Scanner s = new Scanner(System.in);  
System.out.print("given the number: ");  
int a =s.nextInt();  
//function calling  
if (isUntouchable(a))  
System.out.println("it’s an untouchable number. ");  
else  
System.out.println(" it’s not an untouchable number. ");  
}  
}  

Output:

Given the number: 2
It’s an untouchable number.
given the number: 25
It’s not an untouchable number.

// C++ program to demonstrate untouchable number
#include <bits/stdc++.h>
using namespace std;


// Function to determine the sum of all numeral appropriate divisors
int divSum(int a)
{
    // the total of the divisors' sum
    int res = 0;


    // Find all divisors of num
    for (int n = 2; n<= sqrt(a); n++) {


        // If 'n' is divisor of 'num'
        if (a % n == 0) {


            // Add it once if the two divisors are the same; otherwise, add them both.
            if (n == (a / n))
                res += n;
            else
                res += (n + a / n);
        }
    }


    // Given that 1 is also a divisor, add 1 to the result.
    return (res + 1);
}


// Checking whether X is an untouchable number function
bool isUntouchable(int x)
{
    for (int n = 1; n<= 2 * x; n++) {
        if (divSum(n) == x)
            return false;
    }
    return true;
}


// Driver Code
int main()
{
    // Given Number X
    int X = 52;


    // Function Call
    if (isUntouchable(x))
cout<< "Yes";
    else
cout<< "No";
}

Output:

Yes