There is one friendly number and N unfriendly numbers. We want to find how many numbers are there which exactly divide the friendly number, but does not divide any of the unfriendly numbers.

UnfriendlyNumbers.java

public class UnfriendlyNumbers {
	private static long  gcd(long a, long b){
		if(b==0) return a;
		else return gcd(b,a%b);
	}
	public static long calc(long[]arr, long k){
		HashSet<Long> hs= new HashSet<Long>();
		for(int i=0;i<arr.length;i++){
			hs.add(gcd(arr[i],k));
		}
		int count=0;
		long div1;
		long div2;
		boolean flag=false;
		for(int i=1;i<=Math.sqrt(k);i++){
		    if(k%i==0){
		    	div1=i;
		    	div2=k/i;
		        for(long h:hs){
		            if(h%div1 == 0){
		                flag=true;
		                break;
		            }
		        }
		        if(flag==false) count++;
		        flag=false;
		        if(div1!=div2){
		                for(long h:hs){
		                    if(h%div2 == 0){
		                        flag=true;
		                        break;
		                    }
		                }
		                if(flag==false) count++;
		                flag=false;
		        }
		    }
		}
		return count;
	}
    	public static void main(String[] args) throws FileNotFoundException {
		Scanner in = new Scanner(System.in);
	        int n=in.nextInt();
	        long k=Long.parseLong(in.next());
	        long []arr= new long[n];
	        for(int i=0;i<n;i++){
	        	arr[i]=Long.parseLong(in.next());
	        }
	        System.out.print(calc1(arr,k));
	}
}

UnfriendlyNumbersTest.java

public class UnfriendlyNumbersTest {
	@Test
	public void testCalc() {
		assertEquals(1, UnfriendlyNumbers.calc(new long[]{2, 5, 7, 4, 3, 8, 3, 18}, 16));
		assertEquals(0, UnfriendlyNumbers.calc(new long[]{2, 4, 16}, 16));
	}
}