Sphenic Number in Java

In this section, we will learn what is a sphenic number is and show you how to write Java programmes to determine if a specific number are sphenic or not. The sphenic number programme is a common question in academic settings and Java coding exams.

Sphenic Number

If the sum of the factors of a specific number (n) is precisely three and all of the factors are prime, the number is said to be sphenic. Alternatively, n=p x q x r is true if n is a sphenic integer (p, q, and are three distinct prime numbers and their product are n). The OEIS lists the sequence as A007304. Let's use an illustration to help us comprehend.

If the sum of three different prime numbers produces the number, then the number is a sphenic number. There are precisely 8 divisors for the sphenic numbers.

Java implementation of the sphenic number

The 8 divisors are almost as follows:

1. 1
2. Three different primes
3. 3 semi-primes (in which each of the distinct prime factors of the sphenic number is omitted)
4. The sphenic value itself

Take the number 42 to determine whether it is sphenic or otherwise.

1, 2, 3, 7, and 21 make up the number 42's components. Let's discover the eight divisors.

• 21 is equal to 3 times 7 with 2 left out.
• 3 is left out when multiplying 2 by 7 to get 14.
• 7 is left out when multiplying 6 by 2 and 3.
• 42 by itself.

As a result, 42 seems to be a sphenic number since it contains exactly three prime factors—2, 3, and 7—and that number itself is the product of these factors.

Notably, there are 8 divisors inside the cube of the a prime and then another prime, as well as in the seventh powers of primes.

Sphenic Number Illustration

Let's examine whether the number 30 was sphenic or not.

2, 3, and 5 are the fewest three prime factors that add up to the same number. When we multiply them, we arrive at the same result: 30. The supplied number is therefore a sphenic number.

Take another one, 110.

110=1,2,5,10,11,22,55, and 110

2, 5, and 11 are the fewest three prime factors that produce the same numbers. We obtain the very same number 110 when we multiply them. The supplied number is therefore a sphenic number.

Take another, 23, for example.

23=1,23

23 is provided, despite the fact that it isn't sphenic number. mainly due to the two prime elements' simplicity.

We may also verify other numbers in a similar manner. 78, 102, 105, 110, 285, 286, 290, 310, 318, 322, 345, etc. are some other sphenic numbers. The comprehensive list of all sphenic stats up to 10,000 is available from OEIS.

Java program for Sphenic Number

The sphenic numbers has roughly eight divisors, as we discussed before. Therefore, our initial goal is to determine whether the number has exactly 8 divisors or otherwise.

SphenicNumberDemo1.java

import java.util.*;  
public class SphenicNumberDemo1  
{  
// generate a 100000 element global array
static boolean arr[] = new boolean[10000];  
// identifies all primes with smaller sizes than the limit
static void findThePrime()  
{  
// reflects the truth of all entries 
// In the end, if 'pr' is not a prime, a value in mark[p] will be false, else true.
Arrays.fill(arr, true);  
// Repeat this process for all the numbers to designate the composite nature of their multiples.
for(int pr = 2; pr * pr < 10000; pr++)  
{  
// If pr remains unchanged, it is a prime.
if(arr[pr])  
{  
// all the pr multiples should be updated.
for(int s = pr * 2; s < 10000; s = s + pr)  
arr[s] = false;  
}  
}  
}  
// user-defined function that determines whether or not a given integer is sphenic
static int isSphenic(int M)  
{  
// making an array to hold the 8 multipliers
int []arr3 = new int[8];   
// divisors are counted
int coun = 0;    
int h = 0;  
for(int s = 1; s <= M; s++)    
{  
if(M % s == 0 && coun < 8)    
{  
// increases the number by 1
coun++;  
arr3[h++] = s;  
}  
}  
// Verifies whether there are precisely 8 divisors and 
// whether each integer is a distinct prime number. 
// If yes, returns 1, otherwise returns 0.
if(coun == 8 && (arr[arr3[1]] && arr[arr3[2]] && arr[arr3[3]]))  
return 1;  
return 0;  
}  
//loading the driver code  
public static void main(String args[])  
{  
// executing user-defined code to find prime numbers
findThePrime();  
Scanner sc=new Scanner(System.in);  
System.out.print("Enter the number to check: ");  
// taking a user-provided integer
int m=sc.nextInt();  
int res = isSphenic(m);  
if(res == 1)  
// if the previously mentioned condition is true, prints yes.
System.out.print("Yes, the number given is sphenic.");  
else  
// if the above condition returns false, output is printed as no.
System.out.print("No, the number given is not a sphenic.");  
}  
}  

Output:

Enter the number to check: 165
Yes, the number given is sphenic.