A k-Almost Prime Number is a number having exactly k prime factors (not necessary distinct).

For example,

2, 3, 5, 7, 11 ….(in fact all prime numbers) are 1-Almost Prime Numbers as they have only 1 prime factors (which is themselves).

4, 6, 9…. are 2-Almost Prime Numbers as they have exactly 2 prime factors (4 = 2*2, 6 = 2*3, 9 = 3*3)

Similarly 32 is a 5-Almost Prime Number (32 = 2*2*2*2*2) and so is 72 (2*2*2*3*3)

All the 1-Almost Primes are called as Prime Numbers and all the 2-Almost Prime are called as semi-primes.

The task is to print first n numbers that are k prime.

Examples:

Input : k = 2, n = 5 Output : 4 6 9 10 14 4 has two prime factors, 2 x 2 6 has two prime factors, 2 x 3 Similarly, 9(3 x 3), 10(2 x 5) and 14(2 x 7) Input : k = 10, n = 2 Output : 1024 1536 1024 and 1536 are first two numbers with 10 prime factors.

We iterate natural numbers and keep printing k-primes till the count of printed k-primes is less than or equal to n. To check if a number is k-prime, we find count of prime factors and if the count is k we consider the number as k-prime. Below is C++ implementation.

// Program to print first n numbers that are k-primes #include<bits/stdc++.h> // A function to count all prime factors of a given number int countPrimeFactors(int n) { int count = 0; // Count the number of 2s that divide n while (n%2 == 0) { n = n/2; count++; } // n must be odd at this point. So we can skip one // element (Note i = i +2) for (int i = 3; i <= sqrt(n); i = i+2) { // While i divides n, count i and divide n while (n%i == 0) { n = n/i; count++; } } // This condition is to handle the case whien n is a // prime number greater than 2 if (n > 2) count++; return(count); } // A function to print the first n numbers that are // k-almost primes. void printKAlmostPrimes(int k, int n) { for (int i=1, num=2; i<=n; num++) { // Print this number if it is k-prime if (countPrimeFactors(num) == k) { printf("%d ", num); // Increment count of k-primes printed // so far i++; } } return; } /* Driver program to test above function */ int main() { int n = 10, k = 2; printf("First %d %d-almost prime numbers : \n", n, k); printKAlmostPrimes(k, n); return 0; }

Output :

First 10 2-almost prime numbers : 4 6 9 10 14 15 21 22 25 26

**References:**

https://en.wikipedia.org/wiki/Almost_prime

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