Sphenic Number in Java
In this section, we will learn what is a sphenic number and also create Java programs to check if the given number is sphenic or not. The sphenic number program frequently asked in Java coding tests and academics.
A positive integer n is called a sphenic number if the product of factors of the given number (n) is exactly three and all factors are prime. In other words, if n is a sphenic integer then n=p x q x r (p, q, and are three distinct prime numbers and their product are n). It is a sequence A007304 in the OEIS. Let's understand it through an example.
A number will be a sphenic number if the product of three distinct prime numbers gives the number itself. The sphenic numbers have exactly 8 divisors.
The eight divisors are as follows:
Let's consider the number 42 and check it is sphenic or not.
The factors of 42 are 1, 2, 3, 7, 21. Let's find the 8 divisors.
Hence, 42 is a sphenic number because it has exactly three prime factors 2, 3, and 7 and the product of these factors gives the number itself.
Note: The product of the cube of a prime and another prime as well as seventh powers of primes also has 8 divisors.
Sphenic Number Example
Let's take the number 30 and check if it is sphenic or not.
The smallest three primes factors that form the same numbers are 2, 3, and 5. On multiplying them, we get the same number 30. Hence, the given number is a sphenic number.
Let's take another number, 110.
The smallest three primes factors that form the same numbers are 2, 5, and 11. On multiplying them, we get the same number 110. Hence, the given number is a sphenic number.
Let's take another number, 23.
The given number 23 is not a sphenic number. Because there are only two prime factors.
Similarly, we can check other numbers also. Some other sphenic numbers are 78, 102, 105, 110, 285, 286, 290, 310, 318, 322, 345, etc. We can find the complete list of all the sphenic numbers up to 10000 provided by OEIS.
Sphenic Number Java Program
Above, we have discussed that the sphenic number has exactly 8 divisors. So, first, we will try to find if the number is having exactly 8 divisors or not. After that, we will check that the first, three digits (except 1) are prime or not.
Enter a number to check: 165 Yes, the given number is sphenic.
Enter a number to check: 18967 No, the given number is not a sphenic.
Let's find all the sphenic numbers between the given range.
Let's create another Java program to find all the sphenic numbers by using different logic.