正好有3个除数的数字

给定数字N，请打印从1到N范围内的所有数字，其中正好有3个除数。

例子：

Input : N = 16
Output : 4 9
4 and 9 have exactly three divisors.
Divisor

Input : N = 49
Output : 4 9 25 49
4, 9, 25 and 49 have exactly three divisors.

在仔细查看了上面提到的示例之后，您已经注意到，所有必需的数字都是完美的平方，并且也仅是质数。这样做的逻辑是，这样的数字只能有三个数字作为它们的除数，并且还包括1，并且该数字本身仅导致除一个数字以外的单个除数，因此我们可以轻松地得出结论，要求这些数字是平方的质数，以便它们只能有三个除数(1，数字本身和sqrt(number))。因此所有i(i * i小于等于N)的素数都是三素数。

注意：我们可以使用任何筛子方法有效地生成集合中的所有素数，然后我们应该对所有素数进行素数处理，以使i * i <= N。

下面是上述方法的实现：

C++

// C++ program to print all
// three-primes smaller than
// or equal to n using Sieve
// of Eratosthenes
#include 
using namespace std;
 
// Generates all primes upto n and
// prints their squares
void numbersWith3Divisors(int n)
{
    bool prime[n+1];
    memset(prime, true, sizeof(prime));
    prime[0] = prime[1] = 0;
 
    for (int p = 2; p*p <= n; p++)
    {
        // If prime[p] is not changed,
        // then it is a prime
        if (prime[p] == true)
        {
           // Update all multiples of p
           for (int i = p*2; i <= n; i += p)
              prime[i] = false;
        }
    }
 
    // print squares of primes upto n.
    cout << "Numbers with 3 divisors :\n";
    for (int i=0;  i*i <= n ; i++)
        if (prime[i])
          cout << i*i << " ";
}
 
// Driver program
int main()
{
    // sieve();
    int n = 96;
    numbersWith3Divisors(n);
 
    return 0;
}

Java

// Java program to print all
// three-primes smaller than
// or equal to n using Sieve
// of Eratosthenes
import java.io.*;
import java.util.*;
 
class GFG
{
     
    // Generates all primes upto n
    // and prints their squares
    static void numbersWith3Divisors(int n)
    {
        boolean[] prime = new boolean[n+1];
        Arrays.fill(prime, true);
        prime[0] = prime[1] = false;
  
        for (int p = 2; p*p <= n; p++)
        {
             
            // If prime[p] is not changed,
            // then it is a prime
            if (prime[p] == true)
            {
                // Update all multiples of p
                for (int i=p*2; i<=n; i += p)
                    prime[i] = false;
            }
        }
  
        // print squares of primes upto n
        System.out.println("Numbers with 3 divisors : ");
        for (int i=0;  i*i <= n ; i++)
            if (prime[i])
                System.out.print(i*i + " ");
    }
     
    // Driver program
    public static void main (String[] args)
    {
        int n = 96;
        numbersWith3Divisors(n);
    }
}
 
// Contributed by Pramod Kumar

Python3

# Python3 program to print
# all three-primes smaller than
# or equal to n using Sieve
# of Eratosthenes
 
# Generates all primes upto n
# and prints their squares
def numbersWith3Divisors(n):
  
    prime=[True]*(n+1);
    prime[0] = prime[1] = False;
    p=2;
    while (p*p <= n):
         
        # If prime[p] is not changed,
        # then it is a prime
        if (prime[p] == True):
             
            # Update all multiples of p
            for i in range(p*2,n+1,p):
                prime[i] = False;
        p+=1;
 
    # print squares of primes upto n.
    print("Numbers with 3 divisors :");
    i=0;
    while (i*i <= n):
        if (prime[i]):
            print(i*i,end=" ");
        i+=1;
 
# Driver program
 
n = 96;
numbersWith3Divisors(n);
 
# This code is contributed by mits

C#

// C# program to print all
// three-primes smaller than
// or equal to n using Sieve
// of Eratosthenes
 
class GFG
{
     
    // Generates all primes upto n
    // and prints their squares
    static void numbersWith3Divisors(int n)
    {
        bool[] prime = new bool[n+1];
        prime[0] = prime[1] = true;
 
        for (int p = 2; p*p <= n; p++)
        {
             
            // If prime[p] is not changed,
            // then it is a prime
            if (prime[p] == false)
            {
                // Update all multiples of p
                for (int i = p*2; i <= n; i += p)
                    prime[i] = true;
            }
        }
 
        // print squares of primes upto n
        System.Console.WriteLine("Numbers with 3
                                  divisors : ");
        for (int i=0; i*i <= n ; i++)
            if (!prime[i])
                System.Console.Write(i*i + " ");
    }
     
    // Driver program
    public static void Main()
    {
        int n = 96;
        numbersWith3Divisors(n);
    }
}
 
// This code is Contributed by mits

Javascript

    // Javascript program to print all
    // three-primes smaller than
    // or equal to n using Sieve
    // of Eratosthenes
     
    // Generates all primes upto n and
    // prints their squares
    function numbersWith3Divisors(n)
    {
        let prime = new Array(n+1);
        prime.fill(true);
        prime[0] = prime[1] = 0;
 
        for (let p = 2; p*p <= n; p++)
        {
            // If prime[p] is not changed,
            // then it is a prime
            if (prime[p] == true)
            {
               // Update all multiples of p
               for (let i = p*2; i <= n; i += p)
                  prime[i] = false;
            }
        }
 
        // print squares of primes upto n.
        document.write("Numbers with 3 divisors :" + "</br>");
        for (let i = 0;  i*i <= n ; i++)
            if (prime[i])
              document.write(i*i + " ");
    }
 
    // sieve();
    let n = 96;
    numbersWith3Divisors(n);
     
     // This code is contributed by mukesh07.

输出：

Numbers with 3 divisors :
4 9 25 49 

另一种方法：

要打印从1到N的正整数为3的所有数字，主要计算是查找那些为质数平方且小于或等于该数字的平方。我们可以这样做，如下所示：

1. 启动整数i从2到n的循环。
2. 检查i是否为质数，可以使用isPrime(n)方法轻松完成。
3. 如果i为质数，请检查其平方是否小于或等于给定的数字。仅检查质数平方，因此减少了检查次数。
4. 如果满足上述条件，则将打印该数字，并且循环将继续直到i <= n。

这样，将不需要额外的空间来存储任何东西。

这是上述逻辑的一种实现，无需使用额外的空间；

C++

// C++ program to print all
// three-primes smaller than
// or equal to n without using
// extra space
#include 
using namespace std;
 
void numbersWith3Divisors(int);
bool isPrime(int);
 
// Generates all primes upto n and
// prints their squares
void numbersWith3Divisors(int n)
{
    cout << "Numbers with 3 divisors : "
         << endl;
 
    for(int i = 2; i * i <= n; i++)
    {
         
        // Check prime
        if (isPrime(i))
        {
            if (i * i <= n)
            {
                 
                // Print numbers in
                // the order of
                // occurence
                cout << i * i << " ";
            }
        }
    }
}
 
// Check if a number is prime or not
bool isPrime(int n)
{
    if (n == 0 || n == 1)
        return false;
         
    for(int i = 2; i * i <= n; i++)
    {
        if (n % i == 0)
            return false;
    }
    return true;
}
 
// Driver code
int main()
{
    int n = 122;
 
    numbersWith3Divisors(n);
 
    return 0;
}
 
// This code is contributed by vishu2908

Java

// Java program to print all
// three-primes smaller than
// or equal to n without using
// extra space
import java.util.*;
 
class GFG
{
 
    // 3 divisor logic implementation
    // check if a number is
    // prime or not
    // if it is a prime then
    // check if its square
    // is less than or equal to
    // the given number
    static void numbersWith3Divisors(int n)
    {
        System.out.println("Numbers with 3
                                divisors : ");
 
        for (int i = 2; i * i <= n; i++)
        {
             
            // Check prime
            if (isPrime(i))
            {
                if (i * i <= n)
                {
                     
                    // Print numbers in
                    // the order of
                    // occurence
                    System.out.print(i * i + " ");
                }
            }
        }
    }
                            
    // Check if a number is prime or not
    public static boolean isPrime(int n)
    {
        if (n == 0 || n == 1)
            return false;
        for (int i = 2; i * i <= n; i++)
        {
            if (n % i == 0)
                return false;
        }
        return true;
    }
 
    // Driver program
    public static void main(String[] args)
    {
        int n = 122;
        numbersWith3Divisors(n);
    }
}
 
// Contributed by Parag Pallav Singh

Python3

# Python3 program to print all
# three-primes smaller than
# or equal to n without using
# extra space
 
# 3 divisor logic implementation
# check if a number is  prime or
# not if it is a prime then check
# if its square is less than or
# equal to the given number
def numbersWith3Divisors(n):
 
    print("Numbers with 3 divisors : ")
     
    i = 2
    while i * i <= n:
         
        # Check prime
        if (isPrime(i)):
            if (i * i <= n):
             
                # Print numbers in the order
                # of occurence
                print(i * i, end = " ")
                 
        i += 1
       
# Check if a number is prime or not
def isPrime(n):
 
    if (n == 0 or n == 1):
        return False
     
    i = 2
    while i * i <= n:
        if n % i == 0:
            return False
             
        i += 1
 
    return True
 
# Driver code
n = 122
 
numbersWith3Divisors(n)
 
# This code is contributed by divyesh072019

C＃

// C# program to print all
// three-primes smaller than
// or equal to n without using
// extra space
using System;
 
class GFG{
     
// 3 divisor logic implementation
// check if a number is prime or
// not if it is a prime then check
// if its square is less than or
// equal to the given number
static void numbersWith3Divisors(int n)
{
    Console.WriteLine("Numbers with 3 divisors : ");
 
    for(int i = 2; i * i <= n; i++)
    {
         
        // Check prime
        if (isPrime(i))
        {
            if (i * i <= n)
            {
                 
                // Print numbers in the order
                // of occurence
                Console.Write(i * i + " ");
            }
        }
    }
}
                         
// Check if a number is prime or not
public static bool isPrime(int n)
{
    if (n == 0 || n == 1)
        return false;
         
    for(int i = 2; i * i <= n; i++)
    {
        if (n % i == 0)
            return false;
    }
    return true;
}
 
// Driver code
static void Main()
{
    int n = 122;
     
    numbersWith3Divisors(n);
}
}
 
// This code is contributed by divyeshrabadiya07

Java脚本

    // Javascript program to print all
    // three-primes smaller than
    // or equal to n without using
    // extra space
     
      // 3 divisor logic implementation
    // check if a number is prime or
    // not if it is a prime then check
    // if its square is less than or
    // equal to the given number
    function numbersWith3Divisors(n)
    {
        document.write("Numbers with 3 divisors : ");
 
        for(let i = 2; i * i <= n; i++)
        {
 
            // Check prime
            if (isPrime(i))
            {
                if (i * i <= n)
                {
 
                    // Print numbers in the order
                    // of occurence
                    document.write(i * i + " ");
                }
            }
        }
    }
 
    // Check if a number is prime or not
    function isPrime(n)
    {
        if (n == 0 || n == 1)
            return false;
 
        for(let i = 2; i * i <= n; i++)
        {
            if (n % i == 0)
                return false;
        }
        return true;
    }
     
    let n = 122;
      
    numbersWith3Divisors(n);
 
// This code is contributed by suresh07.

输出：

Numbers with 3 divisors :
4 9 25 49 121