Fibonacci numbers with help of DP

Sphenic Number

A Sphenic Number is a positive integer n which is product of exactly three distinct primes. The first few sphenic numbers are 30, 42, 66, 70, 78, 102, 105, 110, 114, …

Sphenic number can be checked by fact that every sphenic number will have exactly 8 divisor SPHENIC NUMBER
So first We will try to find if the number is having exactly 8 divisors if not then simply answer is no.If there are exactly 8 divisors then we will confirm weather the first 3 digits after 1 are prime or not.
Eg. 30 (sphenic number)
30=p*q*r(i.e p,q and r are three distinct prime no and their product are 30)
the set of divisor is (1,2,3,5,6,10,15,30)

Examples:

30 = 2 × 3 × 5 

Sphenic number can be checked by fact that every sphenic number will have exactly 8 divisor SPHENIC NUMBER
So first We will try to find if the number is having exactly 8 divisors if not then simply answer is no.If there are exactly 8 divisors then we will confirm weather the first 3 digits after 1 are prime or not.
Eg. 30 (sphenic number)
30=p*q*r(i.e p,q and r are three distinct prime no and their product are 30)
the set of divisor is (1,2,3,5,6,10,15,30).

// C++ program to check whether a number is a

// Sphenic number or not

#include<bits/stdc++.h>

using namespace std;

//create a global array of size 10001;

bool arr[1001];

// This functions finds all primes smaller than 'limit' 

// using simple sieve of eratosthenes. 

void simpleSieve() 

{

    // initialize all entries of it as true. A value 

    // in mark[p] will finally be false if 'p' is Not 

    // a prime, else true.

    memset(arr,true,sizeof(arr));

  

    // One by one traverse all numbers so that their 

    // multiples can be marked as composite. 

    for(int p=2;p*p<1001;p++)

    {  

        // If p is not changed, then it is a prime

        if(arr[p])

        {// Update all multiples of p 

            for(int i=p*2;i<1001;i=i+p)

            arr[i]=false;

        }

    }

}

int find_sphene(int N)

{

    int arr1[8]={0};   //to store the 8 divisors

    int count=0;        //to count the number of divisor

    int j=0;

    for(int i=1;i<=N;i++)     

    {

        if(N%i==0 &&count<9)        

        {

            count++;

            arr1[j++]=i;

        }

    }

    //finally check if there re 8 divisor and all the numbers are distinct prime no return 1

    //else return 0

    if(count==8 && (arr[arr1[1]] && arr[arr1[2]] && arr[arr1[3]]))

    return 1;

    return 0;

}

  

// Driver program to test above function 

int main() 

{ 

    int n = 60; 

    simpleSieve();

    int ans=find_sphene(n);

    if(ans)

    cout<<"Yes";

    else

    cout<<"NO";

} 

You can read more about this here  https://en.wikipedia.org/wiki/Sphenic_number
You can also read this article on GFG which is written by me only....
https://www.geeksforgeeks.org/sphenic-number/


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