Count in factors

Count in factors is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Write a program which counts up from 1, displaying each number as the multiplication of its prime factors. For the purpose of this task, $1$ may be shown as itself.

For examle, $2$ is prime, so it would be shown as itself. $6$ is not prime; it would be shown as $2\times 3$. Likewise, 2144 is not prime; it would be shown as $2\times 2\times 2\times 2\times 2\times 67$.

c.f. Prime decomposition

D

Library: uiprimes

Library uiprimes is a homebrew library to generate prime numbers upto the maximum 32bit unsigned integer range 2^32-1, by using a pre-generated bit array of Sieve of Eratosthenes (a dll in size of ~256M bytes :p ).

<lang d>import std.stdio, std.math, std.conv, std.algorithm, std.array, std.string ; import xt.uiprimes ;

pragma(lib, "uiprimes.lib") ;

// function _factorize_ included in uiprimes.lib ulong[] factorize(ulong n) {

   if(n == 0) return [] ;
   if(n == 1) return [1] ;
   ulong[] res ;
   uint limit = cast(uint) (1 + sqrt(n)) ;
   foreach(p; Primes(limit)) {
       if(n == 1) break ;
       if(0UL == (n % p ))
           while((n > 1) && (0UL == (n % p ))) {
               res ~= p ;
               n = n / p ;
           }
   }
   if(n > 1)
       res ~= [n] ;
   return res ;

}

string productStr(T)(T[] nums) {

   return array(map!q{to!string(a)}(nums)).join(" x ") ;

}

void main() {

   foreach(i;1..21)
       writefln("%2d = %s", i, productStr(factorize(i))) ;

}</lang>

J

Solution:Use J's factoring primitive, <lang j>q:</lang> Example (including formatting):<lang j> ('1 : 1',":&> ,"1 ': ',"1 ":@q:) 2+i.10 1 : 1 2 : 2 3 : 3 4 : 2 2 5 : 5 6 : 2 3 7 : 7 8 : 2 2 2 9 : 3 3 10: 2 5 11: 11</lang>

Perl 6

<lang perl6># Define a lazy list of primes.

1. Uses the ... sequence operator with a lambda that calculates
2. the next available prime by using some of the existing list
3. as test divisors, so we never divide by anything that isn't
4. known to be a prime already. This is quite fast.

my @primes := 2, 3, -> $n is copy {

   repeat { $n += 2 } until $n %% none do for @primes -> $p {
       last if $p > sqrt($n);
       $p;
   }
   $n;

} ... *;

1. Finds the factors of the given argument.

multi factors(1) { 1 } multi 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;
   }
 }

}

1. An infinite loop, from 1 incrementing upward.
2. calls factor() with each of 1, 2, 3, etc., receives an
3. array containing that number's factors, and then
4. formats and displays them.

say "$_: ", factors($_).join(" ✕ ") for 1..*;</lang>

The first twenty numbers:

1: 1
2: 2
3: 3
4: 2 ✕ 2
5: 5
6: 2 ✕ 3
7: 7
8: 2 ✕ 2 ✕ 2
9: 3 ✕ 3
10: 2 ✕ 5
11: 11
12: 2 ✕ 2 ✕ 3
13: 13
14: 2 ✕ 7
15: 3 ✕ 5
16: 2 ✕ 2 ✕ 2 ✕ 2
17: 17
18: 2 ✕ 3 ✕ 3
19: 19
20: 2 ✕ 2 ✕ 5

Here we use a multi declaration with a constant parameter to match the degenerate case. We use copy parameters when we wish to reuse the formal parameter as a mutable variable within the function. (Parameters default to readonly in Perl 6.) Note the use of gather/take as the final statement in the function, which is a common Perl 6 idiom to set up a coroutine within a function to return a lazy list on demand.

Note also the '✕' above is not ASCII 'x', but U+2715, MULTIPLICATION X. Perl 6 does Unicode natively.

PicoLisp

This is the 'factor' function from Prime decomposition#PicoLisp. <lang 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) ) ) )

(for N 20

  (prinl N ": " (glue " * " (factor N))) )</lang>

Output:

1: 1
2: 2
3: 3
4: 2 * 2
5: 5
6: 2 * 3
7: 7
8: 2 * 2 * 2
9: 3 * 3
10: 2 * 5
11: 11
12: 2 * 2 * 3
13: 13
14: 2 * 7
15: 3 * 5
16: 2 * 2 * 2 * 2
17: 17
18: 2 * 3 * 3
19: 19
20: 2 * 2 * 5

PureBasic

<lang PureBasic>Procedure Factorize(Number, List Factors())

 Protected I = 3, Max
 ClearList(Factors())
 While Number % 2 = 0
   AddElement(Factors())
   Factors() = 2
   Number / 2
 Wend
 Max = Number
 While I <= Max And Number > 1
   While Number % I = 0
     AddElement(Factors())
     Factors() = I
     Number / I
   Wend
   I + 2
 Wend

EndProcedure

If OpenConsole()

 NewList n()
 For a=1 To 20
   text$=RSet(Str(a),2)+"= "
   Factorize(a,n())
   If ListSize(n())
     ResetList(n())
     While NextElement(n())
       text$ + Str(n())
       If ListSize(n())-ListIndex(n())>1
         text$ + "*"
       EndIf
     Wend
   Else
     text$+Str(a) ; To handle the '1', which is not really a prime...
   EndIf
   PrintN(text$)
 Next a

EndIf</lang>

 1= 1
 2= 2
 3= 3
 4= 2*2
 5= 5
 6= 2*3
 7= 7
 8= 2*2*2
 9= 3*3
10= 2*5
11= 11
12= 2*2*3
13= 13
14= 2*7
15= 3*5
16= 2*2*2*2
17= 17
18= 2*3*3
19= 19
20= 2*2*5

Tcl

This factorization code is based on the same engine that is used in the parallel computation task. <lang tcl>package require Tcl 8.5

namespace eval prime {

   variable primes [list 2 3 5 7 11]
   proc restart {} {

variable index -1 variable primes variable current [lindex $primes end]

   }

   proc get_next_prime {} {

variable primes variable index if {$index < [llength $primes]-1} { return [lindex $primes [incr index]] } variable current while 1 { incr current 2 set p 1 foreach prime $primes { if {$current % $prime} {} else { set p 0 break } } if {$p} { return [lindex [lappend primes $current] [incr index]] } }

   }

   proc factors {num} {

restart set factors [dict create] for {set i [get_next_prime]} {$i <= $num} {} { if {$num % $i == 0} { dict incr factors $i set num [expr {$num / $i}] continue } elseif {$i*$i > $num} { dict incr factors $num break } else { set i [get_next_prime] } } return $factors

   }

   # Produce the factors in rendered form
   proc factors.rendered {num} {

set factorDict [factors $num] if {[dict size $factorDict] == 0} { return 1 } dict for {factor times} $factorDict { lappend v {*}[lrepeat $times $factor] } return [join $v "*"]

   }

}</lang> Demonstration code: <lang tcl>set max 20 for {set i 1} {$i <= $max} {incr i} {

   puts [format "%*d = %s" [string length $max] $i [prime::factors.rendered $i]]

}</lang>