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We are given a prime number let’s say, num and the task is to calculate the count of all the numbers less than 10^6 whose minimum prime factor is equal to num.

Input− num = 7Output− Number of prime factors = 38095Input− num = 3Output− Number of prime factors = 16666

Approach used in the below program is as follows

Input the number let’s say num

Start the loop, from i to 2 and i should be less than or equals to max value and increment the value of i

Inside the loop, check if s_prime[i] = 0

Create the loop, set the j to i * 2 and j should be less than equals to max and set j to j + i

Now check, if s_prime[j] = 1

Set s_prime[j] = 1

Increment s_count[i] by 1

Print the result

#include <bits/stdc++.h> using namespace std; #define MAX 1000000 // a sieve for prime number and // to count the number of prime int s_prime[MAX + 4] = { 0 }, s_count[MAX + 4] = { 0 }; void create_sieve(){ // As 1 is not a prime number s_prime[1] = 1; // creating the sieve for (int i = 2; i <= MAX; i++){ // if i is a prime number if (s_prime[i] == 0){ for (int j = i * 2; j <= MAX; j += i){ // if i is the least prime factor if (s_prime[j] == 0){ // The number j is not a prime s_prime[j] = 1; // counting the numbers whose least prime factor // is i s_count[i]++; } } } } } int main(){ // create the sieve create_sieve(); int N = 7; cout << "Number of prime factors = " << (s_count[N] + 1) << endl; N = 3; cout << "Number of prime factors = " << (s_count[N] + 1) << endl; return 0; }

If we run the above code it will generate the following output −

Number of prime factors = 38095 Number of prime factors = 166667

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