# Almost prime

Almost prime
You are encouraged to solve this task according to the task description, using any language you may know.

A   k-Almost-prime   is a natural number   ${\displaystyle n}$   that is the product of   ${\displaystyle k}$   (possibly identical) primes.

Example

1-almost-primes,   where   ${\displaystyle k=1}$,   are the prime numbers themselves.
2-almost-primes,   where   ${\displaystyle k=2}$,   are the   semiprimes.

Write a function/method/subroutine/... that generates k-almost primes and use it to create a table here of the first ten members of k-Almost primes for   ${\displaystyle 1<=K<=5}$.

This imports the package Prime_Numbers from Prime decomposition#Ada.

`with Prime_Numbers, Ada.Text_IO;  procedure Test_Kth_Prime is    package Integer_Numbers is new      Prime_Numbers (Natural, 0, 1, 2);    use Integer_Numbers;    Out_Length: constant Positive := 10; -- 10 k-th almost primes   N: Positive; -- the "current number" to be checked begin   for K in 1 .. 5 loop      Ada.Text_IO.Put("K =" & Integer'Image(K) &":  ");      N := 2;      for I in 1 .. Out_Length loop	 while Decompose(N)'Length /= K loop	    N := N + 1;	 end loop; -- now N is Kth almost prime;	 Ada.Text_IO.Put(Integer'Image(Integer(N)));	 N := N + 1;      end loop;      Ada.Text_IO.New_Line;   end loop;end Test_Kth_Prime;`
Output:
```K = 1:   2 3 5 7 11 13 17 19 23 29
K = 2:   4 6 9 10 14 15 21 22 25 26
K = 3:   8 12 18 20 27 28 30 42 44 45
K = 4:   16 24 36 40 54 56 60 81 84 88
K = 5:   32 48 72 80 108 112 120 162 168 176
```

## ALGOL 68

Worth noticing is the n(...)(...) picture in the printf and the WHILE ... DO SKIP OD idiom which is quite common in ALgol 68.

`BEGIN   INT examples=10, classes=5;   MODE SEMIPRIME = STRUCT ([examples]INT data, INT count);   [classes]SEMIPRIME semi primes;   PROC num facs = (INT n) INT :COMMENT   Return number of not necessarily distinct prime factors of n.   Not very efficient for large n ...COMMENT   BEGIN      INT tf := 2, residue := n, count := 1;      WHILE tf < residue DO	 INT remainder = residue MOD tf;	 ( remainder = 0 | count +:= 1; residue %:= tf | tf +:= 1 )      OD;      count   END;   PROC update table = (REF []SEMIPRIME table, INT i) BOOL :COMMENT   Add i to the appropriate row of the table, if any, unless that row   is already full. Return a BOOL which is TRUE when all of the table   is full.COMMENT   BEGIN      INT k := num facs(i);      IF k <= classes      THEN	 INT c = 1 + count OF table[k];	 ( c <= examples | (data OF table[k])[c] := i; count OF table[k] := c )      FI;      INT sum := 0;      FOR i TO classes DO sum +:= count OF table[i] OD;      sum < classes * examples   END;   FOR i TO classes DO count OF semi primes[i] := 0 OD;   FOR i FROM 2 WHILE update table (semi primes, i) DO SKIP OD;   FOR i TO classes   DO      printf ((\$"k = ", d, ":", n(examples)(xg(0))l\$, i, data OF semi primes[i]))   ODEND`
Output:
```k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 14 15 21 22 25 26
k = 3: 8 12 18 20 27 28 30 42 44 45
k = 4: 16 24 36 40 54 56 60 81 84 88
k = 5: 32 48 72 80 108 112 120 162 168 176
```

## AutoHotkey

Translation of the C Version

`kprime(n,k) {	p:=2, f:=0	while( (f<k) && (p*p<=n) ) {		while ( 0==mod(n,p) ) {			n/=p			f++		}		p++	}	return f + (n>1) == k} k:=1, results:=""while( k<=5 ) {	i:=2, c:=0, results:=results "k =" k ":"	while( c<10 ) {		if (kprime(i,k)) {			results:=results " " i			c++		}		i++	}	results:=results "`n"	k++} MsgBox % results`

Output (Msgbox):

```k =1: 2 3 5 7 11 13 17 19 23 29
k =2: 4 6 9 10 14 15 21 22 25 26
k =3: 8 12 18 20 27 28 30 42 44 45
k =4: 16 24 36 40 54 56 60 81 84 88
k =5: 32 48 72 80 108 112 120 162 168 176```

## AWK

` # syntax: GAWK -f ALMOST_PRIME.AWKBEGIN {    for (k=1; k<=5; k++) {      printf("%d:",k)      c = 0      i = 1      while (c < 10) {        if (kprime(++i,k)) {          printf(" %d",i)          c++        }      }      printf("\n")    }    exit(0)}function kprime(n,k,  f,p) {    for (p=2; f<k && p*p<=n; p++) {      while (n % p == 0) {        n /= p        f++      }    }    return(f + (n > 1) == k)} `

Output:

```1: 2 3 5 7 11 13 17 19 23 29
2: 4 6 9 10 14 15 21 22 25 26
3: 8 12 18 20 27 28 30 42 44 45
4: 16 24 36 40 54 56 60 81 84 88
5: 32 48 72 80 108 112 120 162 168 176
```

## Befunge

Translation of: C

The extra spaces are to ensure it's readable on buggy interpreters that don't include a space after numeric output.

`1>::48*"= k",,,,02p.":",01v|^ v0!`\*:g40:<p402p300:+1<K| >2g03g`*#v_ 1`03g+02g->|[email protected]>/03g1+03p>vpv+1\.:,*48 <P#|!\g40%g40:<4>:9`>#v_\1^||^>#!1#`+#50#:^#+1,+5>#5\$<|`
Output:
```k = 1 : 2  3  5  7  11  13  17  19  23  29
k = 2 : 4  6  9  10  14  15  21  22  25  26
k = 3 : 8  12  18  20  27  28  30  42  44  45
k = 4 : 16  24  36  40  54  56  60  81  84  88
k = 5 : 32  48  72  80  108  112  120  162  168  176```

## C

`#include <stdio.h> int kprime(int n, int k){	int p, f = 0;	for (p = 2; f < k && p*p <= n; p++)		while (0 == n % p)			n /= p, f++; 	return f + (n > 1) == k;} int main(void){	int i, c, k; 	for (k = 1; k <= 5; k++) {		printf("k = %d:", k); 		for (i = 2, c = 0; c < 10; i++)			if (kprime(i, k)) {				printf(" %d", i);				c++;			} 		putchar('\n');	} 	return 0;}`
Output:
```k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 14 15 21 22 25 26
k = 3: 8 12 18 20 27 28 30 42 44 45
k = 4: 16 24 36 40 54 56 60 81 84 88
k = 5: 32 48 72 80 108 112 120 162 168 176
```

## C++

Translation of: Kotlin
`#include <cstdlib>#include <iostream>#include <sstream>#include <iomanip>#include <list> bool k_prime(unsigned n, unsigned k) {    unsigned f = 0;    for (unsigned p = 2; f < k && p * p <= n; p++)        while (0 == n % p) { n /= p; f++; }    return f + (n > 1 ? 1 : 0) == k;} std::list<unsigned> primes(unsigned k, unsigned n)  {    std::list<unsigned> list;    for (unsigned i = 2;list.size() < n;i++)        if (k_prime(i, k)) list.push_back(i);    return list;} int main(const int argc, const char* argv[]) {    using namespace std;    for (unsigned k = 1; k <= 5; k++) {        ostringstream os("");        const list<unsigned> l = primes(k, 10);        for (list<unsigned>::const_iterator i = l.begin(); i != l.end(); i++)            os << setw(4) << *i;        cout << "k = " << k << ':' << os.str() << endl;    } 	return EXIT_SUCCESS;}`
Output:
```k = 1:   2   3   5   7  11  13  17  19  23  29
k = 2:   4   6   9  10  14  15  21  22  25  26
k = 3:   8  12  18  20  27  28  30  42  44  45
k = 4:  16  24  36  40  54  56  60  81  84  88
k = 5:  32  48  72  80 108 112 120 162 168 176```

## C#

`using System;using System.Collections.Generic;using System.Linq; namespace AlmostPrime{    class Program    {        static void Main(string[] args)        {            foreach (int k in Enumerable.Range(1, 5))            {                KPrime kprime = new KPrime() { K = k };                Console.WriteLine("k = {0}: {1}",                    k, string.Join<int>(" ", kprime.GetFirstN(10)));            }        }    }     class KPrime    {        public int K { get; set; }         public bool IsKPrime(int number)        {            int primes = 0;            for (int p = 2; p * p <= number && primes < K; ++p)            {                while (number % p == 0 && primes < K)                {                    number /= p;                    ++primes;                }            }            if (number > 1)            {                ++primes;            }            return primes == K;        }         public List<int> GetFirstN(int n)        {            List<int> result = new List<int>();            for (int number = 2; result.Count < n; ++number)            {                if (IsKPrime(number))                {                    result.Add(number);                }            }            return result;        }    }}`
Output:
```k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 14 15 21 22 25 26
k = 3: 8 12 18 20 27 28 30 42 44 45
k = 4: 16 24 36 40 54 56 60 81 84 88
k = 5: 32 48 72 80 108 112 120 162 168 176
```

## Clojure

`  (ns clojure.examples.almostprime	(:gen-class)) (defn divisors [n]    " Finds divisors by looping through integers 2, 3,...i.. up to sqrt (n) [note: rather than compute sqrt(), test with i*i <=n] "    (let [div (some #(if (= 0 (mod n %)) % nil) (take-while #(<= (* % %) n) (iterate inc 2)))]        (if div                                                         ; div = nil (if no divisor found else its the divisor)             (into [] (concat (divisors div) (divisors (/ n div))))      ; Concat the two divisors of the two divisors            [n])))                                                      ; Number is prime so only itself as a divisor (defn divisors-k [k n]    " Finds n numbers with k divisors.  Does this by looping through integers 2, 3, ... filtering (passing) ones with k divisors and       taking the first n "    (->> (iterate inc 2)            ; infinite sequence of numbers starting at 2         (map divisors)             ; compute divisor of each element of sequence         (filter #(= (count %) k))  ; filter to take only elements with k divisors         (take n)                   ; take n elements from filtered sequence         (map #(apply * %))))       ; compute number by taking product of divisors (println (for [k (range 1 6)]          (println "k:" k (divisors-k k 10)))) }`
Output:
```(k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 14 15 21 22 25 26
k = 3: 8 12 18 20 27 28 30 42 44 45
k = 4: 16 24 36 40 54 56 60 81 84 88
k = 5: 32 48 72 80 108 112 120 162 168 176)
nil
```

## Common Lisp

`(defun start ()  (loop for k from 1 to 5    do (format t "k = ~a: ~a~%" k (collect-k-almost-prime k)))) (defun collect-k-almost-prime (k &optional (d 2) (lst nil))  (cond ((= (length lst) 10) (reverse lst))        ((= (?-primality d) k) (collect-k-almost-prime k (+ d 1) (cons d lst)))        (t (collect-k-almost-prime k (+ d 1) lst)))) (defun ?-primality (n &optional (d 2) (c 0))  (cond ((> d (isqrt n)) (+ c 1))        ((zerop (rem n d)) (?-primality (/ n d) d (+ c 1)))        (t (?-primality n (+ d 1) c))))`
Output:
```k = 1: (2 3 5 7 11 13 17 19 23 29)
k = 2: (4 6 9 10 14 15 21 22 25 26)
k = 3: (8 12 18 20 27 28 30 42 44 45)
k = 4: (16 24 36 40 54 56 60 81 84 88)
k = 5: (32 48 72 80 108 112 120 162 168 176)
NIL```

## D

This contains a copy of the function `decompose` from the Prime decomposition task.

`import std.stdio, std.algorithm, std.traits; Unqual!T[] decompose(T)(in T number) pure nothrowin {    assert(number > 1);} body {    typeof(return) result;    Unqual!T n = number;     for (Unqual!T i = 2; n % i == 0; n /= i)        result ~= i;    for (Unqual!T i = 3; n >= i * i; i += 2)        for (; n % i == 0; n /= i)            result ~= i;     if (n != 1)        result ~= n;    return result;} void main() {    enum outLength = 10; // 10 k-th almost primes.     foreach (immutable k; 1 .. 6) {        writef("K = %d: ", k);        auto n = 2; // The "current number" to be checked.        foreach (immutable i; 1 .. outLength + 1) {            while (n.decompose.length != k)                n++;            // Now n is K-th almost prime.            write(n, " ");            n++;        }        writeln;    }}`
Output:
```K = 1: 2 3 5 7 11 13 17 19 23 29
K = 2: 4 6 9 10 14 15 21 22 25 26
K = 3: 8 12 18 20 27 28 30 42 44 45
K = 4: 16 24 36 40 54 56 60 81 84 88
K = 5: 32 48 72 80 108 112 120 162 168 176```

## EchoLisp

Small numbers : filter the sequence [ 2 .. n]

` (define (almost-prime? p k)	(= k (length (prime-factors p)))) (define (almost-primes k nmax)	(take (filter (rcurry almost-prime? k) [2 ..]) nmax)) (define (task (kmax 6) (nmax 10))	(for ((k [1 .. kmax]))		(write 'k= k '|)		(for-each write (almost-primes k nmax))		(writeln))) `
Output:
` (task) k= 1 | 2 3 5 7 11 13 17 19 23 29k= 2 | 4 6 9 10 14 15 21 22 25 26k= 3 | 8 12 18 20 27 28 30 42 44 45k= 4 | 16 24 36 40 54 56 60 81 84 88k= 5 | 32 48 72 80 108 112 120 162 168 176  `

Large numbers : generate - combinations with repetitions - k-almost-primes up to pmax.

` (lib 'match)(define-syntax-rule (: v i) (vector-ref v i))(reader-infix ':) ;; abbrev (vector-ref v i) === [v : i]  (lib 'bigint)(define cprimes (list->vector (primes 10000))) ;; generates next k-almost-prime < pmax;; c = vector of k primes indices c[i] <= c[j];; p = vector of intermediate products prime[c[0]]*prime[c[1]]*..;; p[k-1] is the generated k-almost-prime;; increment one c[i] at each step (define (almost-next pmax k c p)    (define almost-prime #f)    (define cp 0)     (for ((i (in-range (1- k) -1 -1))) ;; look backwards for c[i] to increment        (vector-set! c i (1+ [c : i])) ;; increment c[i]        (set! cp [cprimes : [c : i]])         (vector-set! p i (if (> i 0) (* [ p : (1- i)] cp) cp)) ;; update partial product         (when (< [p : i) pmax)	    (set! almost-prime            (and  ;; set followers to c[i] value	       (for ((j (in-range (1+ i) k)))	       (vector-set! c j [c : i])	       (vector-set! p j (*  [ p : (1- j)] cp))	       #:break (>= [p : j] pmax) => #f )	       [p  : (1- k)]	  ) ;; // and	  ) ;; set!	  ) ;; when    #:break almost-prime     ) ;; // for i    almost-prime ) ;; not sorted list of k-almost-primes < pmax(define (almost-primes k nmax)    (define base (expt 2 k)) ;; first one is 2^k    (define pmax (* base nmax))    (define c (make-vector k #0))    (define p (build-vector k (lambda(i) (expt #2 (1+ i)))))     (cons base	(for/list 	((almost-prime (in-producer almost-next pmax k c p )))	 almost-prime)))  `
Output:
` ;; we want  500-almost-primes from the 10000-th.(take (drop (list-sort < (almost-primes 500 10000)) 10000 ) 10) (7241149198492252834202927258094752774597239286103014697435725917649659974371690699721153852986440733637405206125678822081264723636566725108094369093648384 etc ... ;; The first one is 2^497 * 3 * 17 * 347 , same result as Haskell.  `

## Elixir

Translation of: Erlang
`defmodule Factors do  def factors(n), do: factors(n,2,[])   defp factors(1,_,acc), do: acc  defp factors(n,k,acc) when rem(n,k)==0, do: factors(div(n,k),k,[k|acc])  defp factors(n,k,acc)                 , do: factors(n,k+1,acc)   def kfactors(n,k), do: kfactors(n,k,1,1,[])   defp kfactors(_tn,tk,_n,k,_acc) when k == tk+1, do: IO.puts "done! "  defp kfactors(tn,tk,_n,k,acc) when length(acc) == tn do    IO.puts "K: #{k} #{inspect acc}"    kfactors(tn,tk,2,k+1,[])  end  defp kfactors(tn,tk,n,k,acc) do    case length(factors(n)) do      ^k -> kfactors(tn,tk,n+1,k,acc++[n])      _  -> kfactors(tn,tk,n+1,k,acc)    end  endend Factors.kfactors(10,5)`
Output:
```K: 1 [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
K: 2 [4, 6, 9, 10, 14, 15, 21, 22, 25, 26]
K: 3 [8, 12, 18, 20, 27, 28, 30, 42, 44, 45]
K: 4 [16, 24, 36, 40, 54, 56, 60, 81, 84, 88]
K: 5 [32, 48, 72, 80, 108, 112, 120, 162, 168, 176]
done!```

## Erlang

Using the factors function from Prime_decomposition#Erlang.

` -module(factors).                                         -export([factors/1,kfactors/0,kfactors/2]).                factors(N) ->                                                  factors(N,2,[]).                                      factors(1,_,Acc) -> Acc;                                  factors(N,K,Acc) when N rem K == 0 ->                         factors(N div K,K, [K|Acc]);                          factors(N,K,Acc) ->                                           factors(N,K+1,Acc).                                    kfactors() -> kfactors(10,5,1,1,[]).                      kfactors(N,K) -> kfactors(N,K,1,1,[]).                    kfactors(_Tn,Tk,_N,K,_Acc) when K == Tk+1 ->  io:fwrite("Done! ");            kfactors(Tn,Tk,N,K,Acc) when length(Acc) == Tn  ->            io:format("K: ~w ~w ~n", [K, Acc]),                       kfactors(Tn,Tk,2,K+1,[]);                              kfactors(Tn,Tk,N,K,Acc) ->                                    case length(factors(N)) of K ->                            kfactors(Tn,Tk, N+1,K, Acc ++ [ N ] );                     _ ->                                                      kfactors(Tn,Tk, N+1,K, Acc) end.                     `
Output:
```9> factors:kfactors(10,5).
K: 1 [2,3,5,7,11,13,17,19,23,29]
K: 2 [4,6,9,10,14,15,21,22,25,26]
K: 3 [8,12,18,20,27,28,30,42,44,45]
K: 4 [16,24,36,40,54,56,60,81,84,88]
K: 5 [32,48,72,80,108,112,120,162,168,176]
Done! ok
10> factors:kfactors(15,10).
K: 1 [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47]
K: 2 [4,6,9,10,14,15,21,22,25,26,33,34,35,38,39]
K: 3 [8,12,18,20,27,28,30,42,44,45,50,52,63,66,68]
K: 4 [16,24,36,40,54,56,60,81,84,88,90,100,104,126,132]
K: 5 [32,48,72,80,108,112,120,162,168,176,180,200,208,243,252]
K: 6 [64,96,144,160,216,224,240,324,336,352,360,400,416,486,504]
K: 7 [128,192,288,320,432,448,480,648,672,704,720,800,832,972,1008]
K: 8 [256,384,576,640,864,896,960,1296,1344,1408,1440,1600,1664,1944,2016]
K: 9 [512,768,1152,1280,1728,1792,1920,2592,2688,2816,2880,3200,3328,3888,4032]
K: 10 [1024,1536,2304,2560,3456,3584,3840,5184,5376,5632,5760,6400,6656,7776,8064]
Done! ok
```

## ERRE

` PROGRAM ALMOST_PRIME !! for rosettacode.org! !\$INTEGER PROCEDURE KPRIME(N,K->KP)  LOCAL P,F  FOR P=2 TO 999 DO      EXIT IF NOT((F<K) AND (P*P<=N))      WHILE (N MOD P)=0 DO         N/=P         F+=1      END WHILE  END FOR  KP=(F-(N>1)=K)END PROCEDURE BEGIN  PRINT(CHR\$(12);)  !CLS  FOR K=1 TO 5 DO     PRINT("k =";K;":";)     C=0     FOR I=2 TO 999 DO        EXIT IF NOT(C<10)        KPRIME(I,K->KP)        IF KP THEN            PRINT(I;)            C+=1        END IF     END FOR     PRINT  END FOREND PROGRAM `
Output:
```K = 1: 2  3  5  7  11  13  17  19  23  29
K = 2: 4  6  9  10  14  15  21  22  25  26
K = 3: 8  12  18  20  27  28  30  42  44  45
K = 4: 16  24  36  40  54  56  60  81  84  88
K = 5: 32  48  72  80  108  112  120  162  168  176```

## Factor

`USING: formatting fry kernel lists lists.lazy localsmath.combinatorics math.primes.factors math.ranges sequences ;IN: rosetta-code.almost-prime : k-almost-prime? ( n k -- ? )    '[ factors _ <combinations> [ product ] map ]    [ [ = ] curry ] bi any? ; :: first10 ( k -- seq )    10 0 lfrom [ k k-almost-prime? ] lfilter ltake list>array ; 5 [1,b] [ dup first10 "K = %d: %[%3d, %]\n" printf ] each`
Output:
```K = 1: {   2,   3,   5,   7,  11,  13,  17,  19,  23,  29 }
K = 2: {   4,   6,   9,  10,  14,  15,  21,  22,  25,  26 }
K = 3: {   8,  12,  18,  20,  27,  28,  30,  42,  44,  45 }
K = 4: {  16,  24,  36,  40,  54,  56,  60,  81,  84,  88 }
K = 5: {  32,  48,  72,  80, 108, 112, 120, 162, 168, 176 }
```

## FreeBASIC

`' FB 1.05.0 Win64 Function kPrime(n As Integer, k As Integer) As Boolean   Dim f As Integer = 0   For i As Integer = 2 To n     While n Mod i = 0       If f = k Then Return false        f += 1       n \= i     Wend   Next   Return f = kEnd Function Dim As Integer i, c, kFor k = 1 To 5  Print "k = "; k; " : ";  i = 2  c = 0  While c < 10      If kPrime(i, k) Then      Print Using "### "; i;      c += 1    End If    i += 1  Wend  PrintNext PrintPrint "Press any key to quit"Sleep`
Output:
```k =  1 :   2   3   5   7  11  13  17  19  23  29
k =  2 :   4   6   9  10  14  15  21  22  25  26
k =  3 :   8  12  18  20  27  28  30  42  44  45
k =  4 :  16  24  36  40  54  56  60  81  84  88
k =  5 :  32  48  72  80 108 112 120 162 168 176
```

## Frink

`for k = 1 to 5{   n=2   count = 0   print["k=\$k:"]   do   {      if length[factorFlat[n]] == k      {         print[" \$n"]         count = count + 1      }      n = n + 1   } while count < 10    println[]}`

Output:

```k=1: 2 3 5 7 11 13 17 19 23 29
k=2: 4 6 9 10 14 15 21 22 25 26
k=3: 8 12 18 20 27 28 30 42 44 45
k=4: 16 24 36 40 54 56 60 81 84 88
k=5: 32 48 72 80 108 112 120 162 168 176
```

## Futhark

` fun kprime(n: int, k: int): bool =  let (p,f) = (2, 0)  loop ((n, p, f)) = while f < k && p*p <= n do    loop ((n,f)) = while 0 == n % p do      (n/p, f+1)    in (n, p+1, f)  in f + (if n > 1 then 1 else 0) == k fun main(m: int): [][]int =  map (fn k: [10]int =>         let ps = replicate 10 0         loop ((i,c,ps) = (2,0,ps)) = while c < 10 do           if kprime(i,k) then             unsafe let ps[c] = i                    in (i+1, c+1, ps)           else (i+1, c, ps)         in ps)  (map (1+) (iota m)) `

## F#

`let rec genFactor (f, n) =    if f > n then None    elif n % f = 0 then Some (f, (f, n/f))    else genFactor (f+1, n)  let factorsOf (num) =    Seq.unfold (fun (f, n) -> genFactor (f, n)) (2, num) let kFactors k = Seq.unfold (fun n ->    let rec loop m =        if Seq.length (factorsOf m) = k then m        else loop (m+1)    let next = loop n    Some(next, next+1)) 2 [1 .. 5]|> List.iter (fun k ->        printfn "%A" (Seq.take 10 (kFactors k) |> Seq.toList))`
Output:
```[2; 3; 5; 7; 11; 13; 17; 19; 23; 29]
[4; 6; 9; 10; 14; 15; 21; 22; 25; 26]
[8; 12; 18; 20; 27; 28; 30; 42; 44; 45]
[16; 24; 36; 40; 54; 56; 60; 81; 84; 88]
[32; 48; 72; 80; 108; 112; 120; 162; 168; 176]```

## Go

`package main import "fmt" func kPrime(n, k int) bool {    nf := 0    for i := 2; i <= n; i++ {        for n%i == 0 {            if nf == k {                return false            }            nf++            n /= i        }    }    return nf == k} func gen(k, n int) []int {    r := make([]int, n)    n = 2    for i := range r {        for !kPrime(n, k) {            n++        }        r[i] = n        n++    }    return r} func main() {    for k := 1; k <= 5; k++ {        fmt.Println(k, gen(k, 10))    }}`
Output:
```1 [2 3 5 7 11 13 17 19 23 29]
2 [4 6 9 10 14 15 21 22 25 26]
3 [8 12 18 20 27 28 30 42 44 45]
4 [16 24 36 40 54 56 60 81 84 88]
5 [32 48 72 80 108 112 120 162 168 176]
```

## Groovy

`  public class almostprime{public static boolean kprime(int n,int k)  {    int i,div=0;     for(i=2;(i*i <= n) && (div<k);i++)      {        while(n%i==0)          {            n = n/i;            div++;          }      }   return div + ((n > 1)?1:0) == k;  }  public static void main(String[] args)    {      int i,l,k;       for(k=1;k<=5;k++)        {          println("k = " + k + ":");           l = 0;            for(i=2;l<10;i++)              {                if(kprime(i,k))                {                  print(i + " ");                  l++;                }              }          println();        }     }}​ `
Output:
```k = 1:
2 3 5 7 11 13 17 19 23 29
k = 2:
4 6 9 10 14 15 21 22 25 26
k = 3:
8 12 18 20 27 28 30 42 44 45
k = 4:
16 24 36 40 54 56 60 81 84 88
k = 5:
32 48 72 80 108 112 120 162 168 176
```

## GW-BASIC

Translation of: FreeBASIC
Works with: PC-BASIC version any
`10  'Almost prime20  FOR K% = 1 TO 530   PRINT "k = "; K%; ": ";40   LET I% = 250   LET C% = 060   WHILE C% < 10  70    LET AN% = I%: LET AK% = K%: GOSUB 100080    IF ISKPRIME <> 0 THEN PRINT USING "### "; I%;: LET C% = C% + 190    LET I% = I% + 1100  WEND110  PRINT120 NEXT K%130 END 995  ' Check if n (AN%) is a k (AK%) prime1000 LET F% = 01010 FOR II% = 2 TO AN%1020  WHILE AN% MOD II% = 01030   IF F% = AK% THEN LET ISKPRIME = 0: RETURN1040   LET F% = F% + 11050   LET AN% = AN% \ II%1060  WEND1070 NEXT II%1080 LET ISKPRIME = (F% = AK%)1090 RETURN `
Output:
```k =  1 :   2   3   5   7  11  13  17  19  23  29
k =  2 :   4   6   9  10  14  15  21  22  25  26
k =  3 :   8  12  18  20  27  28  30  42  44  45
k =  4 :  16  24  36  40  54  56  60  81  84  88
k =  5 :  32  48  72  80 108 112 120 162 168 176
```

`isPrime :: Integral a => a -> BoolisPrime n = not \$ any ((0 ==) . (mod n)) [2..(truncate \$ sqrt \$ fromIntegral n)] primes :: [Integer]primes = filter isPrime [2..] isKPrime :: (Num a, Eq a) => a -> Integer -> BoolisKPrime 1 n = isPrime nisKPrime k n = any (isKPrime (k - 1)) sprimes  where    sprimes = map fst \$ filter ((0 ==) . snd) \$ map (divMod n) \$ takeWhile (< n) primes kPrimes :: (Num a, Eq a) => a -> [Integer]kPrimes k = filter (isKPrime k) [2..] main :: IO ()main = flip mapM_ [1..5] \$ \k ->  putStrLn \$ "k = " ++ show k ++ ": " ++ (unwords \$ map show (take 10 \$ kPrimes k))`
Output:
```k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 14 15 21 22 25 26
k = 3: 8 12 18 20 27 28 30 42 44 45
k = 4: 16 24 36 40 54 56 60 81 84 88
k = 5: 32 48 72 80 108 112 120 162 168 176```

Larger ks require more complicated methods:

`primes = 2:3:[n | n <- [5,7..], foldr (\p r-> p*p > n || rem n p > 0 && r) 	True (drop 1 primes)] merge aa@(a:as) bb@(b:bs)	| a < b = a:merge as bb	| otherwise = b:merge aa bs -- n-th item is all k-primes not divisible by any of the first n primesnotdivs k = f primes \$ kprimes (k-1) where	f (p:ps) s = map (p*) s : f ps (filter ((/=0).(`mod`p)) s) kprimes k	| k == 1 = primes	| otherwise = f (head ndk) (tail ndk) (tail \$ map (^k) primes) where		ndk = notdivs k		-- tt is the thresholds for merging in next sequence		-- it is equal to "map head seqs", but don't do that		f aa@(a:as) seqs tt@(t:ts)			| a < t = a : f as seqs tt			| otherwise = f (merge aa \$ head seqs) (tail seqs) ts main = do 	-- next line is for task requirement:	mapM_ (\x->print (x, take 10 \$ kprimes x)) [1 .. 5] 	putStrLn "\n10000th to 10100th 500-amost primes:"	mapM_ print \$ take 100 \$ drop 10000 \$ kprimes 500`
Output:
```(1,[2,3,5,7,11,13,17,19,23,29])
(2,[4,6,9,10,14,15,21,22,25,26])
(3,[8,12,18,20,27,28,30,42,44,45])
(4,[16,24,36,40,54,56,60,81,84,88])
(5,[32,48,72,80,108,112,120,162,168,176])

10000th to 10100th 500-amost primes:
7241149198492252834202927258094752774597239286103014697435725917649659974371690699721153852986440733637405206125678822081264723636566725108094369093648384
<...snipped 99 more equally unreadable numbers...>
```

## Icon and Unicon

Works in both languages.

`link "factors" procedure main()    every writes(k := 1 to 5,": ") do        every writes(right(genKap(k),5)\10|"\n")end procedure genKap(k)    suspend (k = *factors(n := seq(q)), n)end`

Output:

```->ap
1:     2    3    5    7   11   13   17   19   23   29
2:     4    6    9   10   14   15   21   22   25   26
3:     8   12   18   20   27   28   30   42   44   45
4:    16   24   36   40   54   56   60   81   84   88
5:    32   48   72   80  108  112  120  162  168  176
->
```

## J

`   (10 {. [:~.[:/:~[:,*/~)^:(i.5)~p:i.10 2  3  5  7  11  13  17  19  23  29 4  6  9 10  14  15  21  22  25  26 8 12 18 20  27  28  30  42  44  4516 24 36 40  54  56  60  81  84  8832 48 72 80 108 112 120 162 168 176`

Explanation:

1. Generate 10 primes.
2. Multiply each of them by the first ten primes
3. Sort and find unique values, take the first ten of those
4. Multiply each of them by the first ten primes
5. Sort and find unique values, take the first ten of those
...

The results of the odd steps in this procedure are the desired result.

## Java

`public class AlmostPrime {    public static void main(String[] args) {        for (int k = 1; k <= 5; k++) {            System.out.print("k = " + k + ":");             for (int i = 2, c = 0; c < 10; i++) {                if (kprime(i, k)) {                    System.out.print(" " + i);                    c++;                }            }             System.out.println("");        }    }     public static boolean kprime(int n, int k) {        int f = 0;        for (int p = 2; f < k && p * p <= n; p++) {            while (n % p == 0) {                n /= p;                f++;            }        }        return f + ((n > 1) ? 1 : 0) == k;    }}`
Output:
```k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 14 15 21 22 25 26
k = 3: 8 12 18 20 27 28 30 42 44 45
k = 4: 16 24 36 40 54 56 60 81 84 88
k = 5: 32 48 72 80 108 112 120 162 168 176
```

## JavaScript

`function almostPrime (n, k) {    var divisor = 2, count = 0    while(count < k + 1 && n != 1) {        if (n % divisor == 0) {            n = n / divisor            count = count + 1        } else {            divisor++        }    }    return count == k} for (var k = 1; k <= 5; k++) {    document.write("<br>k=", k, ": ")    var count = 0, n = 0    while (count <= 10) {        n++        if (almostPrime(n, k)) {            document.write(n, " ")            count++        }    }}`
Output:
```k=1: 2 3 5 7 11 13 17 19 23 29 31
k=2: 4 6 9 10 14 15 21 22 25 26 33
k=3: 8 12 18 20 27 28 30 42 44 45 50
k=4: 16 24 36 40 54 56 60 81 84 88 90
k=5: 32 48 72 80 108 112 120 162 168 176 180 ```

## jq

Works with: jq version 1.4

Infrastructure:

`# Recent versions of jq (version > 1.4) have the following definition of "until":def until(cond; next):  def _until:    if cond then . else (next|_until) end;  _until; # relatively_prime(previous) tests whether the input integer is prime# relative to the primes in the array "previous":def relatively_prime(previous):  . as \$in  | (previous|length) as \$plen  # state: [found, ix]  |  [false, 0]  | until( .[0] or .[1] >= \$plen;           [ (\$in % previous[.[1]]) == 0, .[1] + 1] )  | .[0] | not ; # Emit a stream in increasing order of all primes (from 2 onwards)# that are less than or equal to mx:def primes(mx):   # The helper function, next, has arity 0 for tail recursion optimization;  # it expects its input to be the array of previously found primes:  def next:     . as \$previous     | (\$previous | .[length-1]) as \$last     | if (\$last >= mx) then empty       else ((2 + \$last)       | until( relatively_prime(\$previous) ; . + 2)) as \$nextp       | if \$nextp <= mx         then \$nextp, (( \$previous + [\$nextp] ) | next)	 else empty         end       end;  if mx <= 1 then empty  elif mx == 2 then 2  else (2, 3, ( [2,3] | next))  end; # Return an array of the distinct prime factors of . in increasing orderdef prime_factors:   # Return an array of prime factors of . given that "primes"  # is an array of relevant primes:  def pf(primes):    if . <= 1 then []    else . as \$in    | if (\$in | relatively_prime(primes)) then [\$in]      else reduce primes[] as \$p             ([];              if (\$in % \$p) != 0 then . 	      else . + [\$p] +  ((\$in / \$p) | pf(primes))	      end)      end      | unique    end;   if . <= 1 then []  else . as \$in  | pf( [ primes( (1+\$in) | sqrt | floor)  ] )  end; # Return an array of prime factors of . repeated according to their multiplicities:def prime_factors_with_multiplicities:  # Emit p according to the multiplicity of p  # in the input integer assuming p > 1  def multiplicity(p):    if   .  < p     then empty    elif . == p     then p    elif (. % p) == 0 then       ((./p) | recurse( if (. % p) == 0 then (. / p) else empty end) | p)    else empty    end;   if . <= 1 then []  else . as \$in  | prime_factors as \$primes  | if (\$in|relatively_prime(\$primes)) then [\$in]    else reduce \$primes[]  as \$p           ([];            if (\$in % \$p) == 0 then . + [\$in|multiplicity(\$p)] else . end )    end  end;`

isalmostprime

`def isalmostprime(k): (prime_factors_with_multiplicities | length) == k; # Emit a stream of the first N almost-k primesdef almostprimes(N; k):  if N <= 0 then empty  else    # state [remaining, candidate, answer]    [N, 1, null]    | recurse( if .[0] <= 0 then empty	       elif (.[1] | isalmostprime(k)) then [.[0]-1, .[1]+1, .[1]]	       else [.[0], .[1]+1, null]               end)    | .[2] | select(. != null)  end;`
```The task:
```
`range(1;6) as \$k | "k=\(\$k): \([almostprimes(10;\$k)])"`
Output:
`\$ jq -c -r -n -f Almost_prime.jqk=1: [2,3,5,7,11,13,17,19,23,29]k=2: [4,6,9,10,14,15,21,22,25,26]k=3: [8,12,18,20,27,28,30,42,44,45]k=4: [16,24,36,40,54,56,60,81,84,88]k=5: [32,48,72,80,108,112,120,162,168,176]`

## Julia

Works with: Julia version 0.6
`using Primes isalmostprime(n::Integer, k::Integer) = sum(values(factor(n))) == k function almostprimes(N::Integer, k::Integer) # return first N almost-k primes    P = Vector{typeof(k)}(N)    i = 0; n = 2    while i < N        if isalmostprime(n, k) P[i += 1] = n end        n += 1    end    return Pend for k in 1:5    println("\$k-Almost-primes: ", join(almostprimes(10, k), ", "), "...")end`
Output:
```1-Almost-primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
2-Almost-primes: 4, 6, 9, 10, 14, 15, 21, 22, 25, 26...
3-Almost-primes: 8, 12, 18, 20, 27, 28, 30, 42, 44, 45...
4-Almost-primes: 16, 24, 36, 40, 54, 56, 60, 81, 84, 88...
5-Almost-primes: 32, 48, 72, 80, 108, 112, 120, 162, 168, 176...```

## Lua

`-- Returns boolean indicating whether n is k-almost primefunction almostPrime (n, k)    local divisor, count = 2, 0    while count < k + 1 and n ~= 1 do        if n % divisor == 0 then            n = n / divisor            count = count + 1        else            divisor = divisor + 1        end    end    return count == kend -- Generates table containing first ten k-almost primes for given kfunction kList (k)    local n, kTab = 2^k, {}    while #kTab < 10 do        if almostPrime(n, k) then            table.insert(kTab, n)        end        n = n + 1    end    return kTabend -- Main procedure, displays results from five calls to kList()for k = 1, 5 do    io.write("k=" .. k .. ": ")    for _, v in pairs(kList(k)) do        io.write(v .. ", ")    end    print("...")end`
Output:
```k=1: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...
k=2: 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ...
k=3: 8, 12, 18, 20, 27, 28, 30, 42, 44, 45, ...
k=4: 16, 24, 36, 40, 54, 56, 60, 81, 84, 88, ...
k=5: 32, 48, 72, 80, 108, 112, 120, 162, 168, 176, ...```

## Kotlin

Translation of: Java
`fun Int.k_prime(x: Int): Boolean {    var n = x    var f = 0    var p = 2    while (f < this && p * p <= n) {        while (0 == n % p) { n /= p; f++ }        p++    }    return f + (if (n > 1) 1 else 0) == this} fun Int.primes(n : Int) : List<Int> {    var i = 2    var list = mutableListOf<Int>()    while (list.size < n) {        if (k_prime(i)) list.add(i)        i++    }    return list} fun main(args: Array<String>) {    for (k in 1..5)        println("k = \$k: " + k.primes(10))}`
Output:
```k = 1: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
k = 2: [4, 6, 9, 10, 14, 15, 21, 22, 25, 26]
k = 3: [8, 12, 18, 20, 27, 28, 30, 42, 44, 45]
k = 4: [16, 24, 36, 40, 54, 56, 60, 81, 84, 88]
k = 5: [32, 48, 72, 80, 108, 112, 120, 162, 168, 176]```

## Maple

`AlmostPrimes:=proc(k, numvalues::posint:=10)    local aprimes, i, intfactors;    aprimes := Array([]);    i := 0;     do        i := i + 1;        intfactors := ifactors(i)[2];        intfactors := [seq(seq(intfactors[i][1], j=1..intfactors[i][2]),i = 1..numelems(intfactors))];        if numelems(intfactors) = k then            ArrayTools:-Append(aprimes,i);        end if;    until numelems(aprimes) = 10:    aprimes;end proc:<seq( AlmostPrimes(i), i = 1..5 )>;`
Output:
```[[2, 3, 5, 7, 11, 13, 17, 19, 23, 29],
[4, 6, 9, 10, 14, 15, 21, 22, 25, 26],
[8, 12, 18, 20, 27, 28, 30, 42, 44, 45],
[16, 24, 36, 40, 54, 56, 60, 81, 84, 88],
[32, 48, 72, 80, 108, 112, 120, 162, 168, 176]]```

## Mathematica / Wolfram Language

`kprimes[k_,n_] :=  (* generates a list of the n smallest k-almost-primes *)  Module[{firstnprimes, runningkprimes = {}},  firstnprimes = Prime[Range[n]];  runningkprimes = firstnprimes;  Do[   runningkprimes =      Outer[Times, firstnprimes , runningkprimes ] // Flatten // Union  // Take[#, n] & ;    (* only keep lowest n numbers in our running list *)   , {i, 1, k - 1}];  runningkprimes  ](* now to create table with n=10 and k ranging from 1 to 5 *)Table[Flatten[{"k = " <> ToString[i] <> ": ", kprimes[i, 10]}], {i,1,5}] // TableForm`
Output:
```k = 1: 	2	3	5	7	11	13	17	19	23	29
k = 2: 	4	6	9	10	14	15	21	22	25	26
k = 3: 	8	12	18	20	27	28	30	42	44	45
k = 4: 	16	24	36	40	54	56	60	81	84	88
k = 5: 	32	48	72	80	108	112	120	162	168	176```

## Modula-2

`MODULE AlmostPrime;FROM FormatString IMPORT FormatString;FROM Terminal IMPORT WriteString,WriteLn,ReadChar; PROCEDURE KPrime(n,k : INTEGER) : BOOLEAN;VAR p,f : INTEGER;BEGIN    f := 0;    p := 2;    WHILE (f<k) AND (p*p<=n) DO        WHILE n MOD p = 0 DO            n := n DIV p;            INC(f)        END;        INC(p)    END;    IF n>1 THEN        RETURN f+1 = k    END;    RETURN f = kEND KPrime; VAR    buf : ARRAY[0..63] OF CHAR;    i,c,k : INTEGER;BEGIN    FOR k:=1 TO 5 DO        FormatString("k = %i:", buf, k);        WriteString(buf);         i:=2;        c:=0;        WHILE c<10 DO            IF KPrime(i,k) THEN                FormatString(" %i", buf, i);                WriteString(buf);                INC(c)            END;            INC(i)        END;         WriteLn;    END;     ReadChar;END AlmostPrime.`

## Nim

`proc prime(k: int, listLen: int): seq[int] = result = @[] var  test: int = 2  curseur: int = 0 while curseur < listLen:  var   i: int = 2   compte = 0   n = test  while i <= n:   if (n mod i)==0:    n = n div i    compte += 1   else:    i += 1  if compte == k:   result.add(test)   curseur += 1  test += 1 for k in 1..5: echo "k = ",k," : ",prime(k,10)`
Output:
```k = 1 : @[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
k = 2 : @[4, 6, 9, 10, 14, 15, 21, 22, 25, 26]
k = 3 : @[8, 12, 18, 20, 27, 28, 30, 42, 44, 45]
k = 4 : @[16, 24, 36, 40, 54, 56, 60, 81, 84, 88]
k = 5 : @[32, 48, 72, 80, 108, 112, 120, 162, 168, 176]```

## Objeck

Translation of: C
`class Kth_Prime {  function : native : kPrime(n : Int, k : Int) ~ Bool {    f := 0;    for (p := 2; f < k & p*p <= n; p+=1;) {      while (0 = n % p) {        n /= p; f+=1;      };    };     return f + ((n > 1) ? 1 : 0) = k;  }   function : Main(args : String[]) ~ Nil {    for (k := 1; k <= 5; k+=1;) {      "k = {\$k}:"->Print();       c := 0;      for (i := 2; c < 10; i+=1;) {        if (kPrime(i, k)) {          " {\$i}"->Print();          c+=1;        };      };      '\n'->Print();    };  }}`
Output:
```k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 14 15 21 22 25 26
k = 3: 8 12 18 20 27 28 30 42 44 45
k = 4: 16 24 36 40 54 56 60 81 84 88
k = 5: 32 48 72 80 108 112 120 162 168 176```

## Oforth

`: kprime?( n k -- b )| i |   0 2 n for: i [       while( n i /mod swap 0 = ) [ ->n 1+ ] drop       ]    k == ; : table( k -- [] )| l |   Array new dup ->l   2 while (l size 10 <>) [ dup k kprime? if dup l add then 1+ ]   drop ;`
Output:
```>#[ table .cr ] 5 each
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
[4, 6, 9, 10, 14, 15, 21, 22, 25, 26]
[8, 12, 18, 20, 27, 28, 30, 42, 44, 45]
[16, 24, 36, 40, 54, 56, 60, 81, 84, 88]
[32, 48, 72, 80, 108, 112, 120, 162, 168, 176]
```

## PARI/GP

`almost(k)=my(n); for(i=1,10,while(bigomega(n++)!=k,); print1(n", "));for(k=1,5,almost(k);print)`
Output:
```2, 3, 5, 7, 11, 13, 17, 19, 23, 29,
4, 6, 9, 10, 14, 15, 21, 22, 25, 26,
8, 12, 18, 20, 27, 28, 30, 42, 44, 45,
16, 24, 36, 40, 54, 56, 60, 81, 84, 88,
32, 48, 72, 80, 108, 112, 120, 162, 168, 176,```

## Pascal

Library: primTrial
Works with: Free Pascal
`program AlmostPrime;{\$IFDEF FPC}  {\$Mode Delphi}{\$ENDIF}uses  primtrial;var  i,K,cnt : longWord;BEGIN  K := 1;  repeat    cnt := 0;    i := 2;    write('K=',K:2,':');    repeat      if isAlmostPrime(i,K) then      Begin        write(i:6,' ');        inc(cnt);      end;      inc(i);    until cnt = 9;    writeln;    inc(k);  until k > 10;END.`
output
```K= 1 :    2     3     5     7    11    13    17    19    23    29
K= 2 :    4     6     9    10    14    15    21    22    25    26
K= 3 :    8    12    18    20    27    28    30    42    44    45
K= 4 :   16    24    36    40    54    56    60    81    84    88
K= 5 :   32    48    72    80   108   112   120   162   168   176
K= 6 :   64    96   144   160   216   224   240   324   336   352
K= 7 :  128   192   288   320   432   448   480   648   672   704
K= 8 :  256   384   576   640   864   896   960  1296  1344  1408
K= 9 :  512   768  1152  1280  1728  1792  1920  2592  2688  2816
K=10 : 1024  1536  2304  2560  3456  3584  3840  5184  5376  5632```

## Perl

Using a CPAN module, which is simple and fast:

Library: ntheory
`use ntheory qw/factor/;sub almost {  my(\$k,\$n) = @_;  my \$i = 1;  map { \$i++ while scalar factor(\$i) != \$k; \$i++ } 1..\$n;}say "\$_ : ", join(" ", almost(\$_,10)) for 1..5;`
Output:
```1 : 2 3 5 7 11 13 17 19 23 29
2 : 4 6 9 10 14 15 21 22 25 26
3 : 8 12 18 20 27 28 30 42 44 45
4 : 16 24 36 40 54 56 60 81 84 88
5 : 32 48 72 80 108 112 120 162 168 176
```

or writing everything by hand:

`use strict;use warnings; sub k_almost_prime; for my \$k ( 1 .. 5 ) {	my \$almost = 0;	print join(", ", map {		1 until k_almost_prime ++\$almost, \$k;		"\$almost";	} 1 .. 10), "\n";} sub nth_prime; sub k_almost_prime {	my (\$n, \$k) = @_;	return if \$n <= 1 or \$k < 1;	my \$which_prime = 0;	for my \$count ( 1 .. \$k ) {		while( \$n % nth_prime \$which_prime ) {			++\$which_prime;		}		\$n /= nth_prime \$which_prime;		return if \$n == 1 and \$count != \$k;	}	(\$n == 1) ? 1 : ();} BEGIN {	# This is loosely based on one of the python solutions	# to the RC Sieve of Eratosthenes task.	my @primes = (2, 3, 5, 7);	my \$p_iter = 1;	my \$p = \$primes[\$p_iter];	my \$q = \$p*\$p;	my %sieve;	my \$candidate = \$primes[-1] + 2;	sub nth_prime {		my \$n = shift;		return if \$n < 0;		OUTER: while( \$#primes < \$n ) {			while( my \$s = delete \$sieve{\$candidate} ) {				my \$next = \$s + \$candidate;				\$next += \$s while exists \$sieve{\$next};				\$sieve{\$next} = \$s;				\$candidate += 2;			}			while( \$candidate < \$q ) {				push @primes, \$candidate;				\$candidate += 2;				next OUTER if exists \$sieve{\$candidate};			}			my \$twop = 2 * \$p;			my \$next = \$q + \$twop;			\$next += \$twop while exists \$sieve{\$next};			\$sieve{\$next} = \$twop;			\$p = \$primes[++\$p_iter];			\$q = \$p * \$p;				\$candidate += 2;		}		return \$primes[\$n];	}}`
Output:
```2, 3, 5, 7, 11, 13, 17, 19, 23, 29
4, 6, 9, 10, 14, 15, 21, 22, 25, 26
8, 12, 18, 20, 27, 28, 30, 42, 44, 45
16, 24, 36, 40, 54, 56, 60, 81, 84, 88
32, 48, 72, 80, 108, 112, 120, 162, 168, 176
```

## Perl 6

Translation of: C
Works with: Rakudo version 2015.12
`sub is-k-almost-prime(\$n is copy, \$k) returns Bool {    loop (my (\$p, \$f) = 2, 0; \$f < \$k && \$p*\$p <= \$n; \$p++) {        \$n /= \$p, \$f++ while \$n %% \$p;    }    \$f + (\$n > 1) == \$k;} for 1 .. 5 -> \$k {    say ~.[^10]        given grep { is-k-almost-prime(\$_, \$k) }, 2 .. *}`
Output:
```2 3 5 7 11 13 17 19 23 29
4 6 9 10 14 15 21 22 25 26
8 12 18 20 27 28 30 42 44 45
16 24 36 40 54 56 60 81 84 88
32 48 72 80 108 112 120 162 168 176```

Here is a solution with identical output based on the factors routine from Count_in_factors#Perl_6 (to be included manually until we decide where in the distribution to put it).

`constant @primes = 2, |(3, 5, 7 ... *).grep: *.is-prime; multi sub factors(1) { 1 }multi sub factors(Int \$remainder is copy) {    gather for @primes -> \$factor {        # if remainder < factor², we're done        if \$factor * \$factor > \$remainder {            take \$remainder if \$remainder > 1;            last;        }        # How many times can we divide by this prime?        while \$remainder %% \$factor {            take \$factor;            last if (\$remainder div= \$factor) === 1;        }    }} constant @factory = lazy 0..* Z=> flat (0, 0, map { +factors(\$_) }, 2..*); sub almost(\$n) { map *.key, grep *.value == \$n, @factory } put almost(\$_)[^10] for 1..5;`

## Phix

` -- Naieve stuff, mostly, but coded with enthuiasm!-- Following the idea behind (but not the code from!) the J submission:--  Generate 10 primes (kept in p10)                            -- (print K=1)--  Multiply each of them by the first ten primes --  Sort and find unique values, take the first ten of those    -- (print K=2)--  Multiply each of them by the first ten primes --  Sort and find unique values, take the first ten of those    -- (print K=3)--  ...-- However I just keep a "top 10", using a bubble insertion, and stop --  multiplying as soon as everything else for p10[i] will be too big. -- (as calculated earlier from this routine,--  or that "return 1" in pi() works just fine.)--constant f17={2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59}constant f17={2,3,5,7,11,13,17} function pi(integer n)-- approximates the number of primes less than or equal to n--  if n<=10 then return 4 end if--  -- best estimate--  return floor(n/(log(n)-1))--  if n<=20 then return 1 end if -- (or use a table:)    if n<17 then        for i=1 to length(f17) do            if n<=f17[i] then return i end if        end for    end if--  -- upper bound for n>=17 (Rosser and Schoenfeld 1962):--  return floor(1.25506*n/log(n))    -- lower bound for n>=17 (Rosser and Schoenfeld 1962):    return floor(n/log(n))end function function primes(integer n)-- return the first n prime numbers (tested 0 to 20,000, which took ~86s)sequence primeinteger count = 0integer lowN, highN, midN     -- First, iteratively estimate the sieve size required    lowN = 2*n    highN = n*n+1    while lowN<highN do        midN = floor((lowN+highN)/2)        if pi(midN)>n then            highN = midN        else            lowN = midN+1        end if    end while    -- Then apply standard sieve and store primes as we find    -- them towards the (no longer used) start of the sieve.    prime = repeat(1,highN)    for i=2 to highN do        if prime[i] then            count += 1            prime[count] = i            if count>=n then exit end if            for k=i+i to highN by i do                prime[k] = 0            end for         end if    end for    return prime[1..n]end function procedure display(integer k, sequence kprimes)    printf(1,"%d: ",k)    for i=1 to length(kprimes) do        printf(1,"%5d",kprimes[i])    end for    puts(1,"\n")end procedure function bubble(sequence next, integer v)-- insert v into next (discarding next[\$]), keeping next in ascending order-- (relies on next[1] /always/ being smaller that anything that we insert.)    for i=length(next)-1 to 1 by -1 do        if v>next[i] then            next[i+1] = v            exit        end if        next[i+1] = next[i]    end for    return nextend function procedure almost_prime()sequence p10 = primes(10)sequence apk = p10  -- (almostprime[k])sequence next = repeat(0,length(p10))integer high, test    for k=1 to 5 do        display(k,apk)        if k=5 then exit end if        next = apk        for i=1 to length(p10) do--          next[i] = apk[i]*p10[1]            next[i] = apk[i]*2        end for        high = next[\$]        for i=2 to length(p10) do            for j=1 to length(next) do                test = apk[j]*p10[i]                if not find(test,next) then                    if test>high then exit end if                    next = bubble(next,test)                    high = next[\$]                end if            end for        end for        apk = next    end for    if getc(0) then end ifend procedure     almost_prime()  `
Output:
```1:     2    3    5    7   11   13   17   19   23   29
2:     4    6    9   10   14   15   21   22   25   26
3:     8   12   18   20   27   28   30   42   44   45
4:    16   24   36   40   54   56   60   81   84   88
5:    32   48   72   80  108  112  120  162  168  176
```

and a translation of the C version, with improved variable names and some extra notes

`  function kprime(integer n, integer k)---- returns true if n has exactly k factors---- p is a "pseudo prime" in that 2,3,4,5,6,7,8,9,10,11 will behave --  exactly like 2,3,5,7,11, ie the remainder(n,4)=0 (etc) will never --  succeed because remainder(n,2) would have succeeded twice first.--  Hence for larger n consider replacing p+=1 with p=next_prime(),--  then again, on "" this performs an obscene number of divisions..--integer p = 2,         factors = 0     while factors<k and p*p<=n do        while remainder(n,p)=0 do            n = n/p            factors += 1        end while        p += 1    end while     factors += (n>1)    return factors==kend function procedure almost_primeC()integer nextkprime, count     for k=1 to 5 do        printf(1,"k = %d: ", k);        nextkprime = 2        count = 0        while count<10 do            if kprime(nextkprime, k) then                printf(1," %4d", nextkprime)                count += 1            end if             nextkprime += 1        end while        puts(1,"\n")    end for    if getc(0) then end ifend procedure     almost_primeC() `
Output:
```k = 1:     2    3    5    7   11   13   17   19   23   29
k = 2:     4    6    9   10   14   15   21   22   25   26
k = 3:     8   12   18   20   27   28   30   42   44   45
k = 4:    16   24   36   40   54   56   60   81   84   88
k = 5:    32   48   72   80  108  112  120  162  168  176
```

## PicoLisp

`(de factor (N)   (make      (let         (D 2            L (1 2 2 . (4 2 4 2 4 6 2 6 .))            M (sqrt N) )         (while (>= M D)            (if (=0 (% N D))               (setq M                   (sqrt (setq N (/ N (link D)))) )               (inc 'D (pop 'L)) ) )         (link N) ) ) ) (de almost (N)   (let (X 2  Y 0)      (make         (loop            (when (and (nth (factor X) N) (not (cdr @)))               (link X)               (inc 'Y) )            (T (= 10 Y) 'done)            (inc 'X) ) ) ) ) (for I 5   (println I '-> (almost I) ) ) (bye)`

## Potion

`# Converted from Ckprime = (n, k):  p = 2, f = 0  while (f < k && p*p <= n):    while (0 == n % p):      n /= p      f++.    p++.  n = if (n > 1): 1.      else: 0.  f + n == k. 1 to 5 (k):  "k = " print, k print, ":" print  i = 2, c = 0  while (c < 10):    if (kprime(i, k)): " " print, i print, c++.    i++  .  "" say.`

C and Potion take 0.006s, Perl5 0.028s

## Prolog

`% almostPrime(K, +Take, List) succeeds if List can be unified with the% first Take K-almost-primes.% Notice that K need not be specified.% To avoid having to cache or recompute the first Take primes, we define% almostPrime/3 in terms of almostPrime/4 as follows:%almostPrime(K, Take, List) :-  % Compute the list of the first Take primes:  nPrimes(Take, Primes),     almostPrime(K, Take, Primes, List). almostPrime(1, Take, Primes, Primes). almostPrime(K, Take, Primes, List) :-   generate(2, K),  % generate K >= 2  K1 is K - 1,  almostPrime(K1, Take, Primes, L),  multiplylist( Primes, L, Long),  sort(Long, Sorted), % uniquifies  take(Take, Sorted, List). `
That's it. The rest is machinery. For portability, a compatibility section is included below.
`nPrimes( M, Primes) :- nPrimes( [2], M, Primes). nPrimes( Accumulator, I, Primes) :-	next_prime(Accumulator, Prime),	append(Accumulator, [Prime], Next),	length(Next, N),	( N = I -> Primes = Next; nPrimes( Next, I, Primes)). % next_prime(+Primes, NextPrime) succeeds if NextPrime is the next% prime after a list, Primes, of consecutive primes starting at 2.next_prime([2], 3).next_prime([2|Primes], P) :-	last(Primes, PP),	P2 is PP + 2,	generate(P2, N),	1 is N mod 2,		        % odd	Max is floor(sqrt(N+1)),	% round-off paranoia 	forall( (member(Prime, [2|Primes]),		 (Prime =< Max -> true		 ; (!, fail))), N mod Prime > 0 ),	!,        P = N. % multiply( +A, +List, Answer )multiply( A, [], [] ).multiply( A, [X|Xs], [AX|As] ) :-  AX is A * X,   multiply(A, Xs, As). % multiplylist( L1, L2, List ) succeeds if List is the concatenation of X * L2% for successive elements X of L1.multiplylist( [], B, [] ).multiplylist( [A|As], B, List ) :-   multiply(A, B, L1),   multiplylist(As, B, L2),   append(L1, L2, List). take(N, List, Head) :-   length(Head, N),   append(Head,X,List). `
`%%%%% compatibility section %%%%% :- if(current_prolog_flag(dialect, yap)).generate(Min, I) :- between(Min, inf, I). append([],L,L).append([X|Xs], L, [X|Ls]) :- append(Xs,L,Ls). :- endif. :- if(current_prolog_flag(dialect, swi)).generate(Min, I) :- between(Min, inf, I).:- endif. :- if(current_prolog_flag(dialect, yap)).append([],L,L).append([X|Xs], L, [X|Ls]) :- append(Xs,L,Ls). last([X], X).last([_|Xs],X) :- last(Xs,X). :- endif. :- if(current_prolog_flag(dialect, gprolog)).generate(Min, I) :-   current_prolog_flag(max_integer, Max),  between(Min, Max, I).:- endif. `
Example using SWI-Prolog:
```?- between(1,5,I),
(almostPrime(I, 10, L) -> writeln(L)), fail.

[2,3,5,7,11,13,17,19,23,29]
[4,6,9,10,14,15,21,22,25,26]
[8,12,18,20,27,28,30,42,44,45]
[16,24,36,40,54,56,60,81,84,88]
[32,48,72,80,108,112,120,162,168,176]

?- time( (almostPrime(5, 10, L), writeln(L))).
[32,48,72,80,108,112,120,162,168,176]
% 1,906 inferences, 0.001 CPU in 0.001 seconds (84% CPU, 2388471 Lips)
```

## PureBasic

Translation of: C
`EnableExplicit Procedure.b kprime(n.i, k.i)  Define p.i = 2,         f.i = 0   While f < k And p*p <= n    While n % p = 0      n / p      f + 1          Wend        p + 1  Wend   ProcedureReturn Bool(f + Bool(n > 1) = k) EndProcedure ;___main____If Not OpenConsole("Almost prime")  End -1EndIf Define i.i,       c.i,       k.i For k = 1 To 5  Print("k = " + Str(k) + ":")   i = 2  c = 0  While c < 10        If kprime(i, k)      Print(RSet(Str(i),4))      c + 1    EndIf    i + 1  Wend    PrintN("")Next Input()`
Output:
```k = 1:   2   3   5   7  11  13  17  19  23  29
k = 2:   4   6   9  10  14  15  21  22  25  26
k = 3:   8  12  18  20  27  28  30  42  44  45
k = 4:  16  24  36  40  54  56  60  81  84  88
k = 5:  32  48  72  80 108 112 120 162 168 176```

## Python

This imports Prime decomposition#Python

`from prime_decomposition import decomposefrom itertools import islice, counttry:     from functools import reduceexcept:     pass  def almostprime(n, k=2):    d = decompose(n)    try:        terms = [next(d) for i in range(k)]        return reduce(int.__mul__, terms, 1) == n    except:        return False if __name__ == '__main__':    for k in range(1,6):        print('%i: %r' % (k, list(islice((n for n in count() if almostprime(n, k)), 10))))`
Output:
```1: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
2: [4, 6, 9, 10, 14, 15, 21, 22, 25, 26]
3: [8, 12, 18, 20, 27, 28, 30, 42, 44, 45]
4: [16, 24, 36, 40, 54, 56, 60, 81, 84, 88]
5: [32, 48, 72, 80, 108, 112, 120, 162, 168, 176]```

## R

This uses the function from Prime decomposition#R

`#===============================================================# Find k-Almost-primes# R implementation#===============================================================#---------------------------------------------------------------# Function for prime factorization from Rosetta Code#--------------------------------------------------------------- findfactors <- function(n) {  d <- c()  div <- 2; nxt <- 3; rest <- n  while( rest != 1 ) {    while( rest%%div == 0 ) {      d <- c(d, div)      rest <- floor(rest / div)    }    div <- nxt    nxt <- nxt + 2  }  d} #---------------------------------------------------------------# Find k-Almost-primes#--------------------------------------------------------------- almost_primes <- function(n = 10, k = 5) {   # Set up matrix for storing of the results   res <- matrix(NA, nrow = k, ncol = n)  rownames(res) <- paste("k = ", 1:k, sep = "")  colnames(res) <- rep("", n)   # Loop over k   for (i in 1:k) {     tmp <- 1      while (any(is.na(res[i, ]))) { # Keep looping if there are still missing entries in the result-matrix      if (length(findfactors(tmp)) == i) { # Check number of factors        res[i, which.max(is.na(res[i, ]))] <- tmp      }      tmp <- tmp + 1    }  }  print(res)}`
Output:
```k = 1  2  3  5  7  11  13  17  19  23  29
k = 2  4  6  9 10  14  15  21  22  25  26
k = 3  8 12 18 20  27  28  30  42  44  45
k = 4 16 24 36 40  54  56  60  81  84  88
k = 5 32 48 72 80 108 112 120 162 168 176
```

## Racket

`#lang racket(require (only-in math/number-theory factorize)) (define ((k-almost-prime? k) n)  (= k (for/sum ((f (factorize n))) (cadr f)))) (define KAP-table-values  (for/list ((k (in-range 1 (add1 5))))    (define kap? (k-almost-prime? k))    (for/list ((j (in-range 10)) (i (sequence-filter kap? (in-naturals 1))))      i))) (define (format-table t)  (define longest-number-length    (add1 (order-of-magnitude (argmax order-of-magnitude (cons (length t) (apply append t))))))  (define (fmt-val v) (~a v #:width longest-number-length #:align 'right))  (string-join   (for/list ((r t) (k (in-naturals 1)))     (string-append      (format "║ k = ~a║ " (fmt-val k))      (string-join (for/list ((c r)) (fmt-val c)) "| ")      "║"))   "\n")) (displayln (format-table KAP-table-values))`
Output:
```║ k =   1║   2|   3|   5|   7|  11|  13|  17|  19|  23|  29║
║ k =   2║   4|   6|   9|  10|  14|  15|  21|  22|  25|  26║
║ k =   3║   8|  12|  18|  20|  27|  28|  30|  42|  44|  45║
║ k =   4║  16|  24|  36|  40|  54|  56|  60|  81|  84|  88║
║ k =   5║  32|  48|  72|  80| 108| 112| 120| 162| 168| 176║```

## REXX

### naive version

The method used is to count the number of factors in the number to determine the K-primality.

The first three   k-almost   primes for each   K   group are computed directly   (rather than found).

`/*REXX program  computes and displays  the  first  N  K─almost  primes  from   1 ──► K. */parse arg N K .                                  /*get optional arguments from the C.L. */if N=='' | N==","  then N=10                     /*N  not specified?   Then use default.*/if K=='' | K==","  then K= 5                     /*K   "      "          "   "     "    */                                                 /*W: is the width of K, used for output*/    do m=1  for  K;     \$=2**m;  fir=\$           /*generate & assign 1st K─almost prime.*/    #=1;                if #==N  then leave      /*#: K─almost primes; Enough are found?*/    #=2;                \$=\$  3*(2**(m-1))        /*generate & append 2nd K─almost prime.*/    if #==N  then leave                          /*#: K─almost primes; Enough are found?*/    if m==1  then _=fir + fir                    /* [↓]  gen & append 3rd K─almost prime*/             else do;  _=9 * (2**(m-2));    #=3;    \$=\$  _;    end        do j=_ + m - 1   until #==N              /*process an  K─almost prime  N  times.*/        if factr()\==m  then iterate             /*not the correct  K─almost  prime?    */        #=# + 1;         \$=\$ j                   /*bump K─almost counter; append it to \$*/        end   /*j*/                              /* [↑]   generate  N  K─almost  primes.*/    say right(m, length(K))"─almost ("N') primes:'     \$    end       /*m*/                              /* [↑]  display a line for each K─prime*/exit                                             /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/factr: z=j;                    do f=0  while z// 2==0;  z=z% 2;  end  /*divisible by  2.*/                               do f=f  while z// 3==0;  z=z% 3;  end  /*divisible  "  3.*/                               do f=f  while z// 5==0;  z=z% 5;  end  /*divisible  "  5.*/                               do f=f  while z// 7==0;  z=z% 7;  end  /*divisible  "  7.*/                               do f=f  while z//11==0;  z=z%11;  end  /*divisible  " 11.*/                               do f=f  while z//13==0;  z=z%13;  end  /*divisible  " 13.*/         do p=17  by 6  while  p<=z              /*insure  P  isn't divisible by three. */         parse var  p   ''  -1  _                /*obtain the right─most decimal digit. */                                                 /* [↓]  fast check for divisible by 5. */         if _\==5  then do; do f=f+1  while z//p==0; z=z%p; end;  f=f-1; end  /*÷ by P? */         if _ ==3  then iterate                  /*fast check for  X  divisible by five.*/         x=p+2;             do f=f+1  while z//x==0; z=z%x; end;  f=f-1       /*÷ by X? */         end   /*i*/                             /* [↑]  find all the factors in  Z.    */        if f==0  then return 1                    /*if  prime (f==0),  then return unity.*/                     return f                    /*return to invoker the number of divs.*/`
output   when using the default input:
```1─almost (10) primes: 2 3 5 7 11 13 17 19 23 29
2─almost (10) primes: 4 6 9 10 14 15 21 22 25 26
3─almost (10) primes: 8 12 18 20 27 28 30 42 44 45
4─almost (10) primes: 16 24 36 40 54 56 60 81 84 88
5─almost (10) primes: 32 48 72 80 108 112 120 162 168 176
```
output   when using the input of:     20   12
``` 1─almost (20) primes: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71
2─almost (20) primes: 4 6 9 10 14 15 21 22 25 26 33 34 35 38 39 46 49 51 55 57
3─almost (20) primes: 8 12 18 20 27 28 30 42 44 45 50 52 63 66 68 70 75 76 78 92
4─almost (20) primes: 16 24 36 40 54 56 60 81 84 88 90 100 104 126 132 135 136 140 150 152
5─almost (20) primes: 32 48 72 80 108 112 120 162 168 176 180 200 208 243 252 264 270 272 280 300
6─almost (20) primes: 64 96 144 160 216 224 240 324 336 352 360 400 416 486 504 528 540 544 560 600
7─almost (20) primes: 128 192 288 320 432 448 480 648 672 704 720 800 832 972 1008 1056 1080 1088 1120 1200
8─almost (20) primes: 256 384 576 640 864 896 960 1296 1344 1408 1440 1600 1664 1944 2016 2112 2160 2176 2240 2400
9─almost (20) primes: 512 768 1152 1280 1728 1792 1920 2592 2688 2816 2880 3200 3328 3888 4032 4224 4320 4352 4480 4800
10─almost (20) primes: 1024 1536 2304 2560 3456 3584 3840 5184 5376 5632 5760 6400 6656 7776 8064 8448 8640 8704 8960 9600
11─almost (20) primes: 2048 3072 4608 5120 6912 7168 7680 10368 10752 11264 11520 12800 13312 15552 16128 16896 17280 17408 17920 19200
12─almost (20) primes: 4096 6144 9216 10240 13824 14336 15360 20736 21504 22528 23040 25600 26624 31104 32256 33792 34560 34816 35840 38400
```

### optimized version

This optimized REXX version can be over a hundred times faster than the naive version.

Some of the optimizations are:

•   calculating the first   2(K-1)   K─almost primes for each   K   group
•   generating the primes (up to the limit) instead of dividing by (most) divisors.
•   extending the   up-front   prime divisors in the factr function.

The 1st optimization (bullet) allows the direct computation   (instead of searching)   of all K─almost primes up to the first   odd   prime in the list.

Once the required primes are generated, the finding of the K─almost primes is almost instantaneous.

`/*REXX program  computes and displays  the first    N    K─almost primes from  1 ──► K. */parse arg N K .                                  /*obtain optional arguments from the CL*/if N=='' | N==','  then N=10                     /*N  not specified?   Then use default.*/if K=='' | K==','  then K= 5                     /*K   "      "          "   "     "    */nn=N;  N=abs(N);   w=length(K)                   /*N positive? Then show K─almost primes*/limit= (2**K) * N / 2                            /*this is the limit for most K-primes. */if N==1  then limit=limit * 2                    /*  "   "  "    "    "  a    N    of 1.*/if K==1  then limit=limit * 4                    /*  "   "  "    "    "  a K─prime  " 2.*/if K==2  then limit=limit * 2                    /*  "   "  "    "    "  "    "     " 4.*/if K==3  then limit=limit * 3 % 2                /*  "   "  "    "    "  "    "     " 8.*/call genPrimes  limit + 1                        /*generate primes up to the  LIMIT + 1.*/say 'The highest prime computed: '        @.#        " (under the limit of " limit').'say                                              /* [↓]  define where 1st K─prime is odd*/d.=0;  d.2=  2;  d.3 =  4;  d.4 =  7;  d.5 = 13;  d.6 = 22;  d.7 =  38;   d.8=63       d.9=102;  d.10=168;  d.11=268;  d.12=426;  d.13=673;  d.14=1064d!=0    do m=1  for  K;    d!=max(d!,d.m)            /*generate & assign 1st K─almost prime.*/    mr=right(m,w);     mm=m-1     \$=;           do #=1  to min(N, d!)          /*assign some doubled K─almost primes. */                  \$=\$  d.mm.# * 2                  end   /*#*/    #=#-1    if m==1  then from=2             else from=1 + word(\$, words(\$) )         do j=from   until  #==N                  /*process an  K─almost prime  N  times.*/        if factr()\==m  then iterate             /*not the correct  K─almost  prime?    */        #=#+1;   \$=\$ j                           /*bump K─almost counter; append it to \$*/        end   /*j*/                              /* [↑]   generate  N  K─almost  primes.*/     if nn>0  then say mr"─almost ("N') primes:'     \$             else say '    the last'  mr  "K─almost prime: "   word(\$, words(\$))                                               /* [↓]  assign K─almost primes.*/          do q=1  for #;     d.m.q=word(\$,q)             ;   end  /*q*/          do q=1  for #;  if d.m.q\==d.mm.q*2  then leave;   end  /*q*/                                               /* [↑]  count doubly-duplicates*//*──── say copies('─',40)  'for '   m", "   q-1   'numbers were doubly─duplicated.' ────*//*──── say                                                                          ────*/    end       /*m*/                              /* [↑]  display a line for each K─prime*/exit                                             /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/factr: if #.j\==.  then return #.j       z=j;                                do f=0 while z// 2==0; z=z% 2; end   /*÷ by 2*/                                           do f=f while z// 3==0; z=z% 3; end   /*÷ "  3*/                                           do f=f while z// 5==0; z=z% 5; end   /*÷ "  5*/                                           do f=f while z// 7==0; z=z% 7; end   /*÷ "  7*/                                           do f=f while z//11==0; z=z%11; end   /*÷ " 11*/                                           do f=f while z//13==0; z=z%13; end   /*÷ " 13*/                                           do f=f while z//17==0; z=z%17; end   /*÷ " 17*/                                           do f=f while z//19==0; z=z%19; end   /*÷ " 19*/          do i=9    while  @.i<=z;       [email protected].i    /*divide by some higher primes.        */           do f=f  while z//d==0;   z=z%d;  end  /*is  Z  divisible by the  prime  D ?  */         end   /*i*/                             /* [↑]  find all factors in  Z.        */        if f==0  then f=1;   #.j=f;   return f    /*Is prime (f≡0)?   Then return unity. *//*──────────────────────────────────────────────────────────────────────────────────────*/genPrimes: arg x;             @.=;      @.1=2;     @.2=3;    #.=.;     #=2;     s.#[email protected].#**2             do [email protected].# +2  by 2  to x             /*only find odd primes from here on.   */                do p=2  while s.p<=j             /*divide by some known low odd primes. */                if j//@.p==0  then iterate j     /*Is  J  divisible by X?  Then ¬ prime.*/                end   /*p*/                      /* [↓]  a prime  (J)  has been found.  */             #=#+1;    @.#=j;   #.j=1;   s.#=j*j /*bump prime count, and also assign ···*/             end      /*j*/                      /* ··· the # of factors, prime, prime².*/           return                                /* [↑]  not an optimal prime generator.*/`
output   when using the input of:     20   16
```The highest prime computed:  655357  (under the limit of  655360).

1─almost (20) primes:  2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71
2─almost (20) primes:  4 6 9 10 14 15 21 22 25 26 33 34 35 38 39 46 49 51 55 57
3─almost (20) primes:  8 12 18 20 27 28 30 42 44 45 50 52 63 66 68 70 75 76 78 92
4─almost (20) primes:  16 24 36 40 54 56 60 81 84 88 90 100 104 126 132 135 136 140 150 152
5─almost (20) primes:  32 48 72 80 108 112 120 162 168 176 180 200 208 243 252 264 270 272 280 300
6─almost (20) primes:  64 96 144 160 216 224 240 324 336 352 360 400 416 486 504 528 540 544 560 600
7─almost (20) primes:  128 192 288 320 432 448 480 648 672 704 720 800 832 972 1008 1056 1080 1088 1120 1200
8─almost (20) primes:  256 384 576 640 864 896 960 1296 1344 1408 1440 1600 1664 1944 2016 2112 2160 2176 2240 2400
9─almost (20) primes:  512 768 1152 1280 1728 1792 1920 2592 2688 2816 2880 3200 3328 3888 4032 4224 4320 4352 4480 4800
10─almost (20) primes:  1024 1536 2304 2560 3456 3584 3840 5184 5376 5632 5760 6400 6656 7776 8064 8448 8640 8704 8960 9600
11─almost (20) primes:  2048 3072 4608 5120 6912 7168 7680 10368 10752 11264 11520 12800 13312 15552 16128 16896 17280 17408 17920 19200
12─almost (20) primes:  4096 6144 9216 10240 13824 14336 15360 20736 21504 22528 23040 25600 26624 31104 32256 33792 34560 34816 35840 38400
13─almost (20) primes:  8192 12288 18432 20480 27648 28672 30720 41472 43008 45056 46080 51200 53248 62208 64512 67584 69120 69632 71680 76800
14─almost (20) primes:  16384 24576 36864 40960 55296 57344 61440 82944 86016 90112 92160 102400 106496 124416 129024 135168 138240 139264 143360 153600
15─almost (20) primes:  32768 49152 73728 81920 110592 114688 122880 165888 172032 180224 184320 204800 212992 248832 258048 270336 276480 278528 286720 307200
16─almost (20) primes:  65536 98304 147456 163840 221184 229376 245760 331776 344064 360448 368640 409600 425984 497664 516096 540672 552960 557056 573440 614400
```

## Ring

` for ap = 1 to 5    see "k = " + ap + ":"     aList = []    for n = 1 to 200        num = 0        for nr = 1 to n            if n%nr=0 and isPrime(nr)=1               num = num + 1                pr = nr               while true                     pr = pr * nr                     if n%pr = 0                        num = num + 1                     else exit ok               end ok        next          if (ap = 1 and isPrime(n) = 1) or (ap > 1 and num = ap)           add(aList, n)           if len(aList)=10 exit ok ok     next     for m = 1 to len(aList)           see " " + aList[m]     next      see nlnext func isPrime num     if (num <= 1) return 0 ok     if (num % 2 = 0 and num != 2) return 0 ok     for i = 3 to floor(num / 2) -1 step 2         if (num % i = 0) return 0 ok     next     return 1 `

Output:

```k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 14 15 21 22 25 26
k = 3: 8 12 18 20 27 28 30 42 44 45
k = 4: 16 24 36 40 54 56 60 81 84 88
k = 5: 32 48 72 80 108 112 120 162 168 176
```

## Ruby

`require 'prime' def almost_primes(k=2)  return to_enum(:almost_primes, k) unless block_given?  n = 0  loop do     n += 1    yield n if n.prime_division.map( &:last ).inject( &:+ ) == k  endend (1..5).each{|k| puts almost_primes(k).take(10).join(", ")}`
Output:
```2, 3, 5, 7, 11, 13, 17, 19, 23, 29
4, 6, 9, 10, 14, 15, 21, 22, 25, 26
8, 12, 18, 20, 27, 28, 30, 42, 44, 45
16, 24, 36, 40, 54, 56, 60, 81, 84, 88
32, 48, 72, 80, 108, 112, 120, 162, 168, 176
```
Translation of: J
`require 'prime' p ar = pr = Prime.take(10)4.times{p ar = ar.product(pr).map{|(a,b)| a*b}.uniq.sort.take(10)}`
Output:
```[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
[4, 6, 9, 10, 14, 15, 21, 22, 25, 26]
[8, 12, 18, 20, 27, 28, 30, 42, 44, 45]
[16, 24, 36, 40, 54, 56, 60, 81, 84, 88]
[32, 48, 72, 80, 108, 112, 120, 162, 168, 176]
```

## Rust

`fn is_kprime(n: u32, k: u32) -> bool {    let mut primes = 0;    let mut f = 2;    let mut rem = n;    while primes < k && rem > 1{        while (rem % f) == 0 && rem > 1{            rem /= f;            primes += 1;        }        f += 1;    }    rem == 1 && primes == k} struct KPrimeGen {    k: u32,    n: u32,} impl Iterator for KPrimeGen {    type Item = u32;    fn next(&mut self) -> Option<u32> {        self.n += 1;        while !is_kprime(self.n, self.k) {            self.n += 1;        }        Some(self.n)    }} fn kprime_generator(k: u32) -> KPrimeGen {    KPrimeGen {k: k, n: 1}} fn main() {    for k in 1..6 {        println!("{}: {:?}", k, kprime_generator(k).take(10).collect::<Vec<_>>());    }}`
Output:
```1: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
2: [4, 6, 9, 10, 14, 15, 21, 22, 25, 26]
3: [8, 12, 18, 20, 27, 28, 30, 42, 44, 45]
4: [16, 24, 36, 40, 54, 56, 60, 81, 84, 88]
5: [32, 48, 72, 80, 108, 112, 120, 162, 168, 176]
```

## Scala

`def isKPrime(n: Int, k: Int, d: Int = 2): Boolean = (n, k, d) match {    case (n, k, _) if n == 1 => k == 0    case (n, _, d) if n % d == 0 => isKPrime(n / d, k - 1, d)    case (_, _, _) => isKPrime(n, k, d + 1)} def kPrimeStream(k: Int): Stream[Int] = {    def loop(n: Int): Stream[Int] =        if (isKPrime(n, k)) n #:: loop(n+ 1)        else loop(n + 1)    loop(2)} for (k <- 1 to 5) {    println( s"\$k: [\${ kPrimeStream(k).take(10) mkString " " }]" )}`
Output:
```1: [2 3 5 7 11 13 17 19 23 29]
2: [4 6 9 10 14 15 21 22 25 26]
3: [8 12 18 20 27 28 30 42 44 45]
4: [16 24 36 40 54 56 60 81 84 88]
5: [32 48 72 80 108 112 120 162 168 176]
```

## SequenceL

`import <Utilities/Conversion.sl>;import <Utilities/Sequence.sl>; main(args(2)) :=	let		result := firstNKPrimes(1 ... 5, 10); 		output[i] := "k = " ++ intToString(i) ++ ": " ++ delimit(intToString(result[i]), ' ');	in		delimit(output, '\n'); firstNKPrimes(k, N) := firstNKPrimesHelper(k, N, 2, []); firstNKPrimesHelper(k, N, current, result(1)) :=	let		newResult := result when not isKPrime(k, current) else result ++ [current]; 	in		result when size(result) = N	else		firstNKPrimesHelper(k, N, current + 1, newResult); isKPrime(k, n) := size(primeFactorization(n)) = k;`

Using Prime Decomposition Solution [1]

Output:
```main.exe
"k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 14 15 21 22 25 26
k = 3: 8 12 18 20 27 28 30 42 44 45
k = 4: 16 24 36 40 54 56 60 81 84 88
k = 5: 32 48 72 80 108 112 120 162 168 176"
```

## Sidef

Translation of: Perl 6
`func is_k_almost_prime(n, k) {    for (var (p, f) = (2, 0); (f < k) && (p*p <= n); ++p) {        (n /= p; ++f) while (p `divides` n)    }    n > 1 ? (f.inc == k) : (f == k)} { |k|    var x = 10    say gather {        { |i|            if (is_k_almost_prime(i, k)) {                take(i)                --x == 0 && break            }        } << 1..Inf    }} << 1..5`
Output:
```[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
[4, 6, 9, 10, 14, 15, 21, 22, 25, 26]
[8, 12, 18, 20, 27, 28, 30, 42, 44, 45]
[16, 24, 36, 40, 54, 56, 60, 81, 84, 88]
[32, 48, 72, 80, 108, 112, 120, 162, 168, 176]
```

## Tcl

Works with: Tcl version 8.6
Library: Tcllib (Package: math::numtheory)
`package require Tcl 8.6package require math::numtheory proc firstNprimes n {    for {set result {};set i 2} {[llength \$result] < \$n} {incr i} {	if {[::math::numtheory::isprime \$i]} {	    lappend result \$i	}    }    return \$result} proc firstN_KalmostPrimes {n k} {    set p [firstNprimes \$n]    set i [lrepeat \$k 0]    set c {}     while true {	dict set c [::tcl::mathop::* {*}[lmap j \$i {lindex \$p \$j}]] ""	for {set x 0} {\$x < \$k} {incr x} {	    lset i \$x [set xx [expr {([lindex \$i \$x] + 1) % \$n}]]	    if {\$xx} break	}	if {\$x == \$k} break    }    return [lrange [lsort -integer [dict keys \$c]] 0 [expr {\$n - 1}]]} for {set K 1} {\$K <= 5} {incr K} {    puts "\$K => [firstN_KalmostPrimes 10 \$K]"}`
Output:
```1 => 2 3 5 7 11 13 17 19 23 29
2 => 4 6 9 10 14 15 21 22 25 26
3 => 8 12 18 20 27 28 30 42 44 45
4 => 16 24 36 40 54 56 60 81 84 88
5 => 32 48 72 80 108 112 120 162 168 176
```

## uBasic/4tH

Translation of: C
`Local(3) For [email protected] = 1 To 5  Print "k = ";[email protected];": ";   [email protected]=0   For [email protected] = 2 Step 1 While [email protected] < 10    If FUNC(_kprime ([email protected],[email protected])) Then       [email protected] = [email protected] + 1       Print " ";[email protected];    EndIf  Next   PrintNext End _kprime Param(2)  Local(2)   [email protected] = 0  For [email protected] = 2 Step 1 While ([email protected] < [email protected]) * (([email protected] * [email protected]) < ([email protected] + 1))    Do While ([email protected] % [email protected]) = 0      [email protected] = [email protected] / [email protected]      [email protected] = [email protected] + 1    Loop  NextReturn ([email protected] = ([email protected] + ([email protected] > 1)))`
Output:
```k = 1:  2 3 5 7 11 13 17 19 23 29
k = 2:  4 6 9 10 14 15 21 22 25 26
k = 3:  8 12 18 20 27 28 30 42 44 45
k = 4:  16 24 36 40 54 56 60 81 84 88
k = 5:  32 48 72 80 108 112 120 162 168 176

0 OK, 0:200```

## VBScript

Repurposed the VBScript code for the Prime Decomposition task.

` For k = 1 To 5	count = 0	increment = 1	WScript.StdOut.Write "K" & k & ": "	Do Until count = 10		If PrimeFactors(increment) = k Then			WScript.StdOut.Write increment & " "			count = count + 1		End If		increment = increment + 1	Loop	WScript.StdOut.WriteLineNext Function PrimeFactors(n)	PrimeFactors = 0	arrP = Split(ListPrimes(n)," ")	divnum = n	Do Until divnum = 1		For i = 0 To UBound(arrP)-1			If divnum = 1 Then				Exit For			ElseIf divnum Mod arrP(i) = 0 Then				divnum = divnum/arrP(i) 				PrimeFactors = PrimeFactors + 1			End If		Next	LoopEnd Function Function IsPrime(n)	If n = 2 Then		IsPrime = True	ElseIf n <= 1 Or n Mod 2 = 0 Then		IsPrime = False	Else		IsPrime = True		For i = 3 To Int(Sqr(n)) Step 2			If n Mod i = 0 Then				IsPrime = False				Exit For			End If		Next	End IfEnd Function Function ListPrimes(n)	ListPrimes = ""	For i = 1 To n		If IsPrime(i) Then			ListPrimes = ListPrimes & i & " "		End If	NextEnd Function `
Output:
```K1: 2 3 5 7 11 13 17 19 23 29
K2: 4 6 9 10 14 15 21 22 25 26
K3: 8 12 18 20 27 28 30 42 44 45
K4: 16 24 36 40 54 56 60 81 84 88
K5: 32 48 72 80 108 112 120 162 168 176
```

## Yabasic

Translation of: Lua
`// Returns boolean indicating whether n is k-almost primesub almostPrime(n, k)    local divisor, count     divisor = 2     while(count < (k + 1) and n <> 1)        if not mod(n, divisor) then            n = n / divisor            count = count + 1        else            divisor = divisor + 1        end if    wend    return count = kend sub // Generates table containing first ten k-almost primes for given ksub kList(k, kTab())    local n, i     n = 2^k : i = 1    while(i < 11)        if almostPrime(n, k) then            kTab(i) = n            i = i + 1        end if        n = n + 1    wendend sub // Main procedure, displays results from five calls to kList()dim kTab(10)for k = 1 to 5    print "k = ", k, " : ";    kList(k, kTab())    for n = 1 to 10        print kTab(n), ", ";    next    print "..."next`

## zkl

Translation of: Ruby
Translation of: J

Using the prime generator from task Extensible prime generator#zkl.

Can't say I entirely understand this algorithm. Uses list comprehension to calculate the outer/tensor product (p10 ⊗ ar).

`primes:=Utils.Generator(Import("sieve").postponed_sieve);(p10:=ar:=primes.walk(10)).println();do(4){   (ar=([[(x,y);ar;p10;'*]] : Utils.Helpers.listUnique(_).sort()[0,10])).println();}`
Output:
```L(2,3,5,7,11,13,17,19,23,29)
L(4,6,9,10,14,15,21,22,25,26)
L(8,12,18,20,27,28,30,42,44,45)
L(16,24,36,40,54,56,60,81,84,88)
L(32,48,72,80,108,112,120,162,168,176)
```

## ZX Spectrum Basic

Translation of: AWK
`10 FOR k=1 TO 520 PRINT k;":";30 LET c=0: LET i=140 IF c=10 THEN GO TO 10050 LET i=i+160 GO SUB 100070 IF r THEN PRINT " ";i;: LET c=c+190 GO TO 40100 PRINT 110 NEXT k120 STOP 1000 REM kprime1010 LET p=2: LET n=i: LET f=01020 IF f=k OR (p*p)>n THEN GO TO 11001030 IF n/p=INT (n/p) THEN LET n=n/p: LET f=f+1: GO TO 10301040 LET p=p+1: GO TO 10201100 LET r=(f+(n>1)=k)1110 RETURN`
Output:
```1: 2 3 5 7 11 13 17 19 23 29
2: 4 6 9 10 14 15 21 22 25 26
3: 8 12 18 20 27 28 30 42 44 45
4: 16 24 36 40 54 56 60 81 84 88
5: 32 48 72 80 108 112 120 162 168 176```