A composite magic number is a positive integer which is composite as well as a magic number.

Composite number: A composite number is a number that has more than two factors.

For example: 10

Factors are: 1, 2, 5, 10.

Magic number: A magic number is a number in which the eventual sum of the digits is equal to 1.

For example: 28

2 + 8 = 10.

1 + 0 = 1.

Accept two positive integers ‘m’ and ‘n’, where m is less than n as user input. Display the number of composite magic integers that are in the range between ‘m’ and ‘n’ (both inclusive) and output them along with the frequency, in the format specified below.

Test your program with the sample data and some random data:

**Example 1:**

INPUT:

m = 10

n = 100

OUTPUT:

THE COMPOSITE MAGIC INTEGERS ARE:

10, 28, 46, 55, 64, 82, 91, 100

FREQUENCY OF COMPOSITE MAGIC INTEGERS IS: 8

**Example 2:**

INPUT:

m = 1200

n = 1300

OUTPUT:

THE COMPOSITE MAGIC INTEGERS ARE:

1207, 1216, 1225, 1234, 1243, 1252, 1261, 1270, 1288

FREQUENCY OF COMPOSITE MAGIC INTEGERS IS: 9

**Example 3:**

INPUT:

m = 120

n = 99

OUTPUT:

INVALID INPUT

```
import java.io.*;
class CompositeMagic{
public static void main(String args[])throws IOException{
BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
System.out.print("m = ");
int m = Math.abs(Integer.parseInt(br.readLine()));
System.out.print("n = ");
int n = Math.abs(Integer.parseInt(br.readLine()));
if(m >= n){
System.out.println("INVALID INPUT");
return;
}
int count = 0;
System.out.println("THE COMPOSITE MAGIC INTEGERS ARE:");
for(int i = m; i <= n; i++){
if(isComposite(i) && isMagic(i)){
if(count == 0)
System.out.print(i);
else
System.out.print(", " + i);
count++;
}
}
System.out.println("\nFREQUENCY OF COMPOSITE MAGIC INTEGERS IS: " + count);
}
public static boolean isComposite(int num){
int f = 0;
for(int i = 1; i <= num; i++)
if(num % i == 0)
f++;
return f > 2;
}
public static boolean isMagic(int num){
while(num > 9){
num = sumOfDigits(num);
}
return num == 1;
}
public static int sumOfDigits(int num){
int sum = 0;
while(num != 0){
sum += num % 10;
num /= 10;
}
return sum;
}
}
```

Hello, is the “return f>2” in the isComposite function correct?

Yes, because > is a relational operator, and it returns a boolean value (true/false).

Sir,a program is given which states that:

WAP in java to accept a number and check whether the number is prime or not using recursive function. (Using Scanner class)