# K-Primes (Numbers with k prime factors) in a range

Given three integers A, B and K. We need to find no. of K-prime numbers in the range [A, B]. A number is called K-prime if it has exactly K distinct prime factors.

**Examples:**

Input : A = 4, B = 10, K = 2. Output : 6 10 Given range is [4, 5, 6, 7, 8, 9, 10]. From the above range 6 and 10 have 2 distinct prime factors, 6 = 3*2; 10 = 5*2. Input : A = 14, B = 18, K = 2. Output : 14 15 18 Range = [14, 15]. Both 14, 15 and 18 have 2 distinct prime factors, 14 = 7*2, 15 = 3*5 and 18 = 2*3*3

A **simple solution** is to traverse through given range. For every element of the range, find its prime factors. Finally print all those numbers whose prime factors are k.

An **efficient solution** is to use Sieve Of Eratosthenes Algorithm

prime[n] = {true}; 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; } }

If we observe the above algorithm clearly it has a property of iterating through all the multiples of prime numbers less than N. So the number of times the algorithm marks a number not prime is equal to the number of prime factors of that number. To achieve this, maintain an array called marked and increase the count of a number every time when it is marked as not prime by the algorithm. And in the next step, we iterate through all the numbers in the range [A, B] and increase our count of k-prime numbers if marked[number] == K.

## C++

`// CPP program to count all those numbers in ` `// given range whose count of prime factors ` `// is k ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `void` `printKPFNums(` `int` `A, ` `int` `B, ` `int` `K) ` `{ ` ` ` `// Count prime factors of all numbers ` ` ` `// till B. ` ` ` `bool` `prime[B+1] = { ` `true` `}; ` ` ` `int` `p_factors[B+1] = { 0 }; ` ` ` `for` `(` `int` `p = 2; p <= B; p++) ` ` ` `if` `(p_factors[p] == 0) ` ` ` `for` `(` `int` `i = p; i <= B; i += p) ` ` ` `p_factors[i]++; ` ` ` ` ` `// Print all numbers with k prime factors ` ` ` `for` `(` `int` `i = A; i <= B; i++) ` ` ` `if` `(p_factors[i] == K) ` ` ` `cout << i << ` `" "` `; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `A = 14, B = 18, K = 2; ` ` ` `printKPFNums(A, B, K); ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program to count ` `// all those numbers in ` `// given range whose count ` `// of prime factors ` `// is k ` ` ` `import` `java.io.*; ` `import` `java.util.*; ` ` ` `class` `GFG { ` ` ` ` ` `static` `void` `printKPFNums(` `int` `A, ` `int` `B, ` `int` `K) ` ` ` `{ ` ` ` `// Count prime factors of all numbers ` ` ` `// till B. ` ` ` `boolean` `prime[] = ` `new` `boolean` `[B+` `1` `]; ` ` ` `Arrays.fill(prime,` `true` `); ` ` ` `int` `p_factors[] = ` `new` `int` `[B+` `1` `]; ` ` ` `Arrays.fill(p_factors,` `0` `); ` ` ` ` ` `for` `(` `int` `p = ` `2` `; p <= B; p++) ` ` ` `if` `(p_factors[p] == ` `0` `) ` ` ` `for` `(` `int` `i = p; i <= B; i += p) ` ` ` `p_factors[i]++; ` ` ` ` ` `// Print all numbers with k prime factors ` ` ` `for` `(` `int` `i = A; i <= B; i++) ` ` ` `if` `(p_factors[i] == K) ` ` ` `System.out.print( i + ` `" "` `); ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `main(String args[]) ` ` ` `{ ` ` ` `int` `A = ` `14` `, B = ` `18` `, K = ` `2` `; ` ` ` `printKPFNums(A, B, K); ` ` ` `} ` `} ` ` ` ` ` `// This code is contributed ` `// by Nikita Tiwari. ` |

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## Python3

`# Python 3 program to count ` `# all those numbers in ` `# given range whose count ` `# of prime factors ` `# is k ` ` ` `def` `printKPFNums(A, B, K) : ` ` ` ` ` `# Count prime factors ` ` ` `# of all numbers ` ` ` `# till B. ` ` ` `prime ` `=` `[ ` `True` `]` `*` `(B` `+` `1` `) ` ` ` `p_factors` `=` `[ ` `0` `]` `*` `(B` `+` `1` `) ` ` ` `for` `p ` `in` `range` `(` `2` `,B` `+` `1` `) : ` ` ` `if` `(p_factors[p] ` `=` `=` `0` `) : ` ` ` `for` `i ` `in` `range` `(p,B` `+` `1` `,p) : ` ` ` `p_factors[i] ` `=` `p_factors[i] ` `+` `1` ` ` ` ` `# Print all numbers with ` ` ` `# k prime factors ` ` ` `for` `i ` `in` `range` `(A,B` `+` `1` `) : ` ` ` `if` `(p_factors[i] ` `=` `=` `K) : ` ` ` `print` `( i ,end` `=` `" "` `) ` ` ` ` ` `# Driver code ` `A ` `=` `14` `B ` `=` `18` `K ` `=` `2` `printKPFNums(A, B, K) ` ` ` ` ` `# This code is contributed ` `# by Nikita Tiwari. ` |

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## C#

`// C# program to count all ` `// those numbers in given ` `// range whose count of ` `// prime factors is k ` `using` `System; ` ` ` `class` `GFG { ` ` ` ` ` `static` `void` `printKPFNums(` `int` `A, ` `int` `B, ` ` ` `int` `K) ` ` ` `{ ` ` ` `// Count prime factors of ` ` ` `// all numbers till B. ` ` ` `bool` `[]prime = ` `new` `bool` `[B + 1]; ` ` ` ` ` `for` `(` `int` `i = 0; i < B + 1; i++) ` ` ` `prime[i] = ` `true` `; ` ` ` ` ` `int` `[]p_factors = ` `new` `int` `[B + 1]; ` ` ` ` ` `for` `(` `int` `i = 0; i < B + 1; i++) ` ` ` `p_factors[i] = 0; ` ` ` ` ` `for` `(` `int` `p = 2; p <= B; p++) ` ` ` `if` `(p_factors[p] == 0) ` ` ` `for` `(` `int` `i = p; i <= B; i += p) ` ` ` `p_factors[i]++; ` ` ` ` ` `// Print all numbers with ` ` ` `// k prime factors ` ` ` `for` `(` `int` `i = A; i <= B; i++) ` ` ` `if` `(p_factors[i] == K) ` ` ` `Console.Write( i + ` `" "` `); ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `Main() ` ` ` `{ ` ` ` `int` `A = 14, B = 18, K = 2; ` ` ` `printKPFNums(A, B, K); ` ` ` `} ` `} ` ` ` `// This code is contributed by nitin mittal. ` |

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## PHP

`<?php ` `// PHP program to count all those numbers ` `// in given range whose count of prime ` `// factors is k ` ` ` `function` `printKPFNums(` `$A` `, ` `$B` `, ` `$K` `) ` `{ ` ` ` `// Count prime factors of all ` ` ` `// numbers till B. ` ` ` `$prime` `= ` `array_fill` `(true, ` `$B` `+ 1, NULL); ` ` ` `$p_factors` `= ` `array_fill` `(0, ` `$B` `+ 1, NULL); ` ` ` `for` `(` `$p` `= 2; ` `$p` `<= ` `$B` `; ` `$p` `++) ` ` ` `if` `(` `$p_factors` `[` `$p` `] == 0) ` ` ` `for` `(` `$i` `= ` `$p` `; ` `$i` `<= ` `$B` `; ` `$i` `+= ` `$p` `) ` ` ` `$p_factors` `[` `$i` `]++; ` ` ` ` ` `// Print all numbers with ` ` ` `// k prime factors ` ` ` `for` `(` `$i` `= ` `$A` `; ` `$i` `<= ` `$B` `; ` `$i` `++) ` ` ` `if` `(` `$p_factors` `[` `$i` `] == ` `$K` `) ` ` ` `echo` `$i` `. ` `" "` `; ` `} ` ` ` `// Driver code ` `$A` `= 14; ` `$B` `= 18; ` `$K` `= 2; ` `printKPFNums(` `$A` `, ` `$B` `, ` `$K` `); ` ` ` `// This code is contributed ` `// by ChitraNayal ` `?> ` |

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**Output:**

14 15 18

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