The nth Catalan number in terms of binomial coefficients is calculated by the formula(n + k )/k where k varies from 2 to n and n ≥ 0. i.e.Cn = (2n)!/((n+1)!n!)Programpublic class CatalanNumbers {    public static long fact(int i) {       if(i

A composite number whose sum of digits equal to the sum of the digits of its prime factors.Ex: 58 = 2 x 29 (5 + 8 = 12) (2+ 2 + 9 = 12)Programpublic class SmithNumbers {    public static boolean isPrime(int number) {       int loop;       int prime = 1;       for(loop = 2; loop < number; loop++) {          if((number % loop) == 0) {             prime = 0;          }       }       if (prime ... Read More

A composite number whose sum of digits equal to the sum of the digits of its prime factors.Ex: 58 = 2 x 29 (5 + 8 = 12) (2+ 2 + 9 = 12)Programpublic class SmithNumbers {    public static boolean isPrime(int number) {       int loop;       int prime = 1;       for(loop = 2; loop < number; loop++) {          if((number % loop) == 0) {             prime = 0;          }       }       if (prime ... Read More

Following is the Java program which prints the kth prime factor of a number n, when k and n are given.Programimport java.util.Scanner; public class KthPrimeFactor {    public static void main(String args[]) {       int number, k, factor = 0;       Scanner sc = new Scanner(System.in);       System.out.println("Enter a number :");             number = sc.nextInt();       System.out.println("Enter the k value :");       k = sc.nextInt();       int temp = k-1;             for(int i = 2; i< number; ... Read More

Following is the Java program which prints the kth prime factor of a number n, when k and n are given.Programimport java.util.Scanner; public class KthPrimeFactor {    public static void main(String args[]) {       int number, k, factor = 0;       Scanner sc = new Scanner(System.in);       System.out.println("Enter a number :");             number = sc.nextInt();       System.out.println("Enter the k value :");       k = sc.nextInt();       int temp = k-1;             for(int i = 2; i< number; ... Read More

The numbers which can be expressed as the sum of positive consecutive integers are known as polite numbers.Ex: 5 = 2+3The number of ways a number can be expressed as the sum of positive integers will be the Politeness of that number.Ex: 9 = 4+5 || 2+3+4AlgorithmGet the prime factors of a number.Get the powers of prime factors greater than 2.Add 1 to all of them.Multiply them, subtract 1 from the result.Programimport java.util.Scanner; public class PolitenessOfANumber {    public static void main(String args[]) {       Scanner sc = new Scanner(System.in);       System.out.println("Enter a number");   ... Read More

The numbers which can be expressed as the sum of positive consecutive integers are known as polite numbers.Ex: 5 = 2+3The number of ways a number can be expressed as the sum of positive integers will be the Politeness of that number.Ex: 9 = 4+5 || 2+3+4AlgorithmGet the prime factors of a number.Get the powers of prime factors greater than 2.Add 1 to all of them.Multiply them, subtract 1 from the result.Programimport java.util.Scanner; public class PolitenessOfANumber {    public static void main(String args[]) {       Scanner sc = new Scanner(System.in);       System.out.println("Enter a number");   ... Read More

Following is the Java program which prints all the sum of all the divisors of a given number.

Following is the Java program which prints all the sum of all the divisors of a given number.

Following is the Java program which prints all the divisors of a given number.Programimport java.util.Scanner; public class DivisorsOfNaturalNumber {    public static void main(String args[]) {       Scanner sc = new Scanner(System.in);       System.out.println("Enter required number :");       int num = sc.nextInt();             for(int i = 1; i