Anti-primes

From Rosetta Code
Task
Anti-primes
You are encouraged to solve this task according to the task description, using any language you may know.

The anti-primes (or highly composite numbers, sequence A002182 in the OEIS) are the natural numbers with more factors than any smaller than itself.


Task

Generate and show here, the first twenty anti-primes.


Related tasks



11l[edit]

V max_divisors = 0
V c = 0
V n = 1
L
   V divisors = 1
   L(i) 1 .. n I/ 2
      I n % i == 0
         divisors++

   I divisors > max_divisors
      max_divisors = divisors
      print(n, end' ‘ ’)
      c++
      I c == 20
         L.break

   n++
Output:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

8086 Assembly[edit]

puts:	equ	9	; MS-DOS print string syscall
amount:	equ	20 	; Amount of antiprimes to find
	cpu	8086
	org	100h
	xor	si,si	; SI = current number
	xor	cx,cx	; CH = max # of factors, CL = # of antiprimes
cand:	inc	si	
 	mov	di,si	; DI = maximum factor to test
	shr	di,1
	mov	bp,1	; BP = current candidate
	xor	bl,bl	; BL = factor count
.test:	mov	ax,si	; Test current candidate 
	xor	dx,dx
	div	bp
	test	dx,dx	; Evenly divisible?
	jnz	.next
	inc	bx	; Then increment factors
.next:	inc	bp	; Next possible factor
	cmp	bp,si	; Are we there yet?
	jbe	.test	; If not, try next factor
	cmp	bl,ch	; Is it an antiprime?
	jbe	cand	; If not, next candidate
	inc	cx	; If so, increment the amount of antiprimes seen
	mov	ch,bl	; Update maximum amount of factors
	mov	bx,nbuf	; Convert current number to ASCII
	mov	ax,si
	mov	di,10
digit:	xor	dx,dx	; Extract a digit
	div	di
	add	dl,'0'	; Add ASCII 0
	dec	bx
	mov 	[bx],dl	; Store it
	test	ax,ax	; Any more digits?
	jnz	digit	; If so, get next digit
	mov	dx,bx
	mov	ah,puts
	int	21h	; Print using MS-DOS
	cmp 	cl,amount	; Do we need any more antiprimes?
	jb	cand	; If so, find the next one
	ret		; Otherwise, back to DOS
	db	'.....'	; Placeholder for decimal output
nbuf:	db	' $'
Output:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560 

AArch64 Assembly[edit]

Works with: as version Raspberry Pi 3B version Buster 64 bits
or android 64 bits with application Termux
/* ARM assembly AARCH64 Raspberry PI 3B */
/*  program antiprime64.s   */
 
/************************************/
/* Constantes                       */
/************************************/
.include "../includeConstantesARM64.inc" 
 
.equ NMAXI,      20
.equ MAXLINE,     5
/*********************************/
/* Initialized data              */
/*********************************/
.data
sMessResult:        .asciz " @ "
szCarriageReturn:   .asciz "\n"
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss  
sZoneConv:                  .skip 24
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main 
main:                             // entry of program 
    ldr x3,qNMaxi                 // load limit
    mov x5,#0                     // maxi
    mov x6,#0                     // result counter
    mov x7,#0                     // display counter
    mov x4,#1                     // number begin
1:
    mov x0,x4                     // number
    bl decFactor                  // compute number factors
    cmp x0,x5                     // maxi ?
    cinc x4,x4,le                 // no -> increment indice
    //addle x4,x4,#1                // no -> increment indice
    ble 1b                        // and loop
    mov x5,x0
    mov x0,x4
    bl displayResult
    add x7,x7,#1                  // increment display counter
    cmp x7,#MAXLINE               // line maxi ?
    blt 2f
    mov x7,#0
    ldr x0,qAdrszCarriageReturn
    bl affichageMess              // display message
2:
    add x6,x6,#1                  // increment result counter
    add x4,x4,#1                  // increment number
    cmp x6,x3                     // end ?
    blt 1b
 
100:                              // standard end of the program 
    mov x0, #0                    // return code
    mov x8,EXIT 
    svc #0                        // perform the system call
qAdrszCarriageReturn:        .quad szCarriageReturn
qNMaxi:                       .quad NMAXI
/***************************************************/
/*   display message number                        */
/***************************************************/
/* x0 contains number 1           */
/* x1 contains number 2               */
displayResult:
    stp x1,lr,[sp,-16]!        // save  registers 
    ldr x1,qAdrsZoneConv
    bl conversion10            // call décimal conversion
    ldr x0,qAdrsMessResult
    ldr x1,qAdrsZoneConv       // insert conversion in message
    bl strInsertAtCharInc
    
    bl affichageMess           // display message
    ldp x1,lr,[sp],16          // restaur  registers 
    ret
qAdrsMessResult:     .quad sMessResult
qAdrsZoneConv:       .quad sZoneConv
/***************************************************/
/*   compute factors sum                        */
/***************************************************/
/* x0 contains the number            */
decFactor:
    stp x1,lr,[sp,-16]!       // save  registers 
    stp x2,x3,[sp,-16]!       // save  registers 
    stp x4,x5,[sp,-16]!       // save  registers 
    mov x5,#0                 // init number factors
    mov x4,x0                 // save number
    mov x1,#1                 // start factor -> divisor
1:
    mov x0,x4                 // dividende
    udiv x2,x0,x1
    msub x3,x2,x1,x0
    cmp x1,x2                 // divisor > quotient ?
    bgt 3f
    cmp x3,#0                 // remainder = 0 ?
    bne 2f
    add x5,x5,#1              // increment counter factors
    cmp x1,x2                 // divisor = quotient ?
    beq 3f                    // yes -> end
    add x5,x5,#1              // no -> increment counter factors
2:
    add x1,x1,#1              // increment factor
    b 1b                      // and loop
3:
    mov x0,x5                 // return counter
    ldp x4,x5,[sp],16 // restaur  registers 
    ldp x2,x3,[sp],16 // restaur  registers 
    ldp x1,lr,[sp],16  // restaur  registers
    ret 
/***************************************************/
/*      ROUTINES INCLUDE                           */
/***************************************************/
.include "../includeARM64.inc"
 1  2  4  6  12
 24  36  48  60  120
 180  240  360  720  840
 1260  1680  2520  5040  7560

Action![edit]

BYTE FUNC CountDivisors(INT a)
  INT i
  BYTE prod,count

  prod=1 count=0
  WHILE a MOD 2=0
  DO
    count==+1
    a==/2
  OD
  prod==*(1+count)

  i=3
  WHILE i*i<=a
  DO
    count=0
    WHILE a MOD i=0
    DO
      count==+1
      a==/i
    OD
    prod==*(1+count)
    i==+2
  OD

  IF a>2 THEN
    prod==*2
  FI
RETURN (prod)

PROC Main()
  BYTE toFind=[20],found=[0],count,max=[0]
  INT i=[1]

  PrintF("The first %B Anti-primes are:%E",toFind)
  WHILE found<toFind
  DO
    count=CountDivisors(i)
    IF count>max THEN
      max=count
      found==+1
      PrintI(i)
      IF found<toFind THEN
        Print(", ")
      FI
    FI
    i==+1
  OD
RETURN
Output:

Screenshot from Atari 8-bit computer

The first 20 Anti-primes are:
1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560

Ada[edit]

with Ada.Text_IO; use Ada.Text_IO;

procedure Antiprimes is

   function Count_Divisors (N : Integer) return Integer is
      Count : Integer := 1;
   begin
      for i in 1 .. N / 2 loop
         if N mod i = 0 then
            Count := Count + 1;
         end if;
      end loop;
      return Count;
   end Count_Divisors;

   Results      : array (1 .. 20) of Integer;
   Candidate    : Integer := 1;
   Divisors     : Integer;
   Max_Divisors : Integer := 0;

begin
   for i in Results'Range loop
      loop
         Divisors := Count_Divisors (Candidate);
         if Max_Divisors < Divisors then
            Results (i)  := Candidate;
            Max_Divisors := Divisors;
            exit;
         end if;
         Candidate := Candidate + 1;
      end loop;
   end loop;
   Put_Line ("The first 20 anti-primes are:");
   for I in Results'Range loop
      Put (Integer'Image (Results (I)));
   end loop;
   New_Line;
end Antiprimes;
Output:
The first 20 anti-primes are:
 1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

ALGOL 68[edit]

BEGIN # find some anti-primes: numbers with more divisors than the     #
      # previous numbers                                               #
    INT max number   := 10 000;
    INT max divisors := 0;
    # construct a table of the divisor counts                          #
    [ 1 : max number ]INT ndc; FOR i FROM 1 TO UPB ndc DO ndc[ i ] := 1 OD;
    FOR i FROM 2 TO UPB ndc DO
        FOR j FROM i BY i TO UPB ndc DO ndc[ j ] +:= 1 OD
    OD;
    # show the numbers with more divisors than their predecessors      #
    INT a count := 0;
    FOR i TO UPB ndc WHILE a count < 20 DO
        INT divisor count = ndc[ i ];
        IF divisor count > max divisors THEN
            print( ( " ", whole( i, 0 ) ) );
            max divisors := divisor count;
            a count     +:= 1
        FI
    OD;
    print( ( newline ) )
END
Output:
 1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

ALGOL W[edit]

begin
    % find some anti-primes - numbers with more factors than the numbers    %
    % smaller than them                                                     %
    % calculates the number of divisors of v                                %
    integer procedure divisor_count( integer value v ) ; begin
        integer total, n, p;
        total := 1; n := v;
        while not odd( n ) do begin
            total := total + 1;
            n     := n div 2
        end while_not_odd_n ;
        p := 3;
        while ( p * p ) <= n do begin
            integer count;
            count := 1;
            while n rem p = 0 do begin
                count := count + 1;
                n     := n div p
            end while_n_rem_p_eq_0 ;
            p     := p + 2;
            total := total * count
        end while_p_x_p_le_n ;
        if n > 1 then total := total * 2;
        total
    end divisor_count ;
    begin
        integer maxAntiPrime, antiPrimeCount, maxDivisors, n;
        maxAntiPrime := 20;
        n := maxDivisors := antiPrimeCount := 0;
        while antiPrimeCount < maxAntiPrime do begin
            integer divisors;
            n := n + 1;
            divisors := divisor_count( n );
            if divisors > maxDivisors then begin
                writeon( i_w := 1, s_w := 0, " ", n );
                maxDivisors    := divisors;
                antiPrimeCount := antiPrimeCount + 1
            end if_have_an_anti_prime
        end while_antiPrimeCoiunt_lt_maxAntiPrime
    end
end.
Output:
 1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

AppleScript[edit]

on factorCount(n)
    set counter to 0
    set sqrt to n ^ 0.5
    set limit to sqrt div 1
    if (limit = sqrt) then
        set counter to counter + 1
        set limit to limit - 1
    end if
    repeat with i from limit to 1 by -1
        if (n mod i is 0) then set counter to counter + 2
    end repeat
    
    return counter
end factorCount

on antiprimes(howMany)
    set output to {}
    set mostFactorsSoFar to 0
    set n to 0
    repeat until ((count output) = howMany)
        set n to n + 1
        tell (factorCount(n))
            if (it > mostFactorsSoFar) then
                set end of output to n
                set mostFactorsSoFar to it
            end if
        end tell
    end repeat
    
    return output
end antiprimes

antiprimes(20)
Output:
{1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560}

APL[edit]

Works in Dyalog APL

f{⍸≠⌈\(∪⊢∨⍳)¨}
Output:
      f 8000
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

ARM Assembly[edit]

Works with: as version Raspberry Pi
or android 32 bits with application Termux
/* ARM assembly Raspberry PI or android with termux */
/*  program antiprime.s   */
 
 /* REMARK 1 : this program use routines in a include file 
   see task Include a file language arm assembly 
   for the routine affichageMess conversion10 
   see at end of this program the instruction include */
/* for constantes see task include a file in arm assembly */
/************************************/
/* Constantes                       */
/************************************/
.include "../constantes.inc"
 
.equ NMAXI,      20
.equ MAXLINE,     5
/*********************************/
/* Initialized data              */
/*********************************/
.data
sMessResult:        .asciz " @ "
szCarriageReturn:   .asciz "\n"
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss  
sZoneConv:                  .skip 24
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main 
main:                             @ entry of program 
    ldr r3,iNMaxi                 @ load limit
    mov r5,#0                     @ maxi
    mov r6,#0                     @ result counter
    mov r7,#0                     @ display counter
    mov r4,#1                     @ number begin
1:
    mov r0,r4                     @ number
    bl decFactor                  @ compute number factors
    cmp r0,r5                     @ maxi ?
    addle r4,r4,#1                @ no -> increment indice
    ble 1b                        @ and loop
    mov r5,r0
    mov r0,r4
    bl displayResult
    add r7,r7,#1                  @ increment display counter
    cmp r7,#MAXLINE               @ line maxi ?
    blt 2f
    mov r7,#0
    ldr r0,iAdrszCarriageReturn
    bl affichageMess              @ display message
2:
    add r6,r6,#1                  @ increment result counter
    add r4,r4,#1                  @ increment number
    cmp r6,r3                     @ end ?
    blt 1b
 
100:                              @ standard end of the program 
    mov r0, #0                    @ return code
    mov r7, #EXIT                 @ request to exit program
    svc #0                        @ perform the system call
iAdrszCarriageReturn:        .int szCarriageReturn
iNMaxi:                       .int NMAXI
/***************************************************/
/*   display message number                        */
/***************************************************/
/* r0 contains number 1           */
/* r1 contains number 2               */
displayResult:
    push {r1,lr}               @ save registers 
    ldr r1,iAdrsZoneConv
    bl conversion10            @ call décimal conversion
    ldr r0,iAdrsMessResult
    ldr r1,iAdrsZoneConv       @ insert conversion in message
    bl strInsertAtCharInc
    
    bl affichageMess           @ display message
    pop {r1,pc}                @ restaur des registres
iAdrsMessResult:     .int sMessResult
iAdrsZoneConv:       .int sZoneConv
/***************************************************/
/*   compute factors sum                        */
/***************************************************/
/* r0 contains the number            */
decFactor:
    push {r1-r5,lr}           @ save registers 
    mov r5,#0                 @ init number factors
    mov r4,r0                 @ save number
    mov r1,#1                 @ start factor -> divisor
1:
    mov r0,r4                 @ dividende
    bl division
    cmp r1,r2                 @ divisor > quotient ?
    bgt 3f
    cmp r3,#0                 @ remainder = 0 ?
    bne 2f
    add r5,r5,#1              @ increment counter factors
    cmp r1,r2                 @ divisor = quotient ?
    beq 3f                    @ yes -> end
    add r5,r5,#1              @ no -> increment counter factors
2:
    add r1,r1,#1              @ increment factor
    b 1b                      @ and loop
3:
    mov r0,r5                 @ return counter
    pop {r1-r5,pc}            @ restaur registers

/***************************************************/
/*      ROUTINES INCLUDE                           */
/***************************************************/
.include "../affichage.inc"
 1            2            4            6            12
 24           36           48           60           120
 180          240          360          720          840
 1260         1680         2520         5040         7560

Arturo[edit]

found: 0
i: 1
maxDiv: 0

while [found<20][
    fac: size factors i
    if fac > maxDiv [
        print i
        maxDiv: fac
        found: found + 1
    ]
    i: i + 1
]
Output:
1
2
4
6
12
24
36
48
60
120
180
240
360
720
840
1260
1680
2520
5040
7560

AWK[edit]

Translation of: Go
# syntax: GAWK -f ANTI-PRIMES.AWK
BEGIN {
    print("The first 20 anti-primes are:")
    while (count < 20) {
      d = count_divisors(++n)
      if (d > max_divisors) {
        printf("%d ",n)
        max_divisors = d
        count++
      }
    }
    printf("\n")
    exit(0)
}
function count_divisors(n,  count,i) {
    if (n < 2) {
      return(1)
    }
    count = 2
    for (i=2; i<=n/2; i++) {
      if (n % i == 0) {
        count++
      }
    }
    return(count)
}
Output:
The first 20 anti-primes are:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

BASIC[edit]

BASIC256[edit]

Dim Results(20)
Candidate = 1
max_divisors = 0

Print "Los primeros 20 anti-primos son:"
For j = 0 To 19
	Do
		divisors = count_divisors(Candidate)
		If max_divisors < divisors Then
			Results[j] = Candidate
			max_divisors = divisors
			Exit Do
		End If
		Candidate += 1
	Until false
	Print Results[j];" ";
Next j

Function count_divisors(n)
	cont = 1
	For i = 1 To n/2
		If (n % i) = 0 Then cont += 1
	Next i
	count_divisors = cont
End Function
Output:
Los primeros 20 anti-primos son:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

FreeBASIC[edit]

' convertido desde Ada
Declare Function count_divisors(n As Integer) As Integer

Dim As Integer max_divisors, divisors, results(1 To 20), candidate, j
candidate = 1

Function count_divisors(n As Integer) As Integer
    Dim As Integer i, count = 1
    For i = 1 To n/2
        If (n Mod i) = 0 Then count += 1
    Next i
    count_divisors = count
End Function

Print "Los primeros 20 anti-primos son:"
For j = 1 To 20
    Do
        divisors = count_divisors(Candidate)
        If max_divisors < divisors Then
            Results(j) = Candidate
            max_divisors = divisors
            Exit Do
        End If
        Candidate += 1
    Loop
Next j
For j = 1 To 20
    Print Results(j);
Next j
Print
Sleep
Output:
Los primeros 20 anti-primos son:
 1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

GW-BASIC[edit]

Works with: BASICA
10 REM Anti-primes
20 DEFINT A-Z
30 N=1
40 IF S>=20 THEN END ELSE F=1
50 IF N<2 GOTO 80 ELSE FOR I=1 TO N\2
60 IF N MOD I=0 THEN F=F+1
70 NEXT
80 IF F<=M GOTO 120
90 PRINT N,
100 M=F
110 S=S+1
120 N=N+1
130 GOTO 40
Output:
 1             2             4             6             12
 24            36            48            60            120
 180           240           360           720           840
 1260          1680          2520          5040          7560

Another solution:

Works with: BASICA
10 REM Anti-primes
20 C = -999
30 N = N + 1
40 GOSUB 70
50 IF T = 20 THEN END
60 GOTO 30
70 D = 0
80 FOR F = 1 TO INT(N/2)
90 IF N MOD F = 0 THEN D = D + 1
100 NEXT F
110 IF D > C THEN GOSUB 130
120 RETURN
130 C = D
140 T = T + 1
150 PRINT N
160 RETURN
Output:
 1
 2
 4
 6
 12
 24
 36
 48
 60
 120
 180
 240
 360
 720
 840
 1260
 1680
 2520
 5040
 7560

PureBasic[edit]

Translation of: C
Procedure.i cntDiv(n.i)
  Define.i i, count  
  If n < 2 : ProcedureReturn 1 : EndIf  
  count = 2 : i = 2  
  While i <= n / 2    
    If n % i = 0 : count + 1 : EndIf
    i + 1
  Wend  
  ProcedureReturn count
EndProcedure

; - - - MAIN - - - 
Define.i n = 1, d, maxDiv = 0, count = 0
If OpenConsole("")
  PrintN("The first 20 anti-primes are: ")      
  While count < 20    
    d = cntDiv(n)
    If d > maxDiv
      Print(Str(n) + " ")
      maxDiv = d : count + 1
    EndIf
    n + 1
  Wend  
  PrintN("")
  Input()
EndIf
End 0
Output:
The first 20 anti-primes are: 
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560 

QuickBASIC[edit]

Translation of: ALGOL W
' Anti-primes
DECLARE FUNCTION DivisorCount (V%)

MaxAntiPrime% = 20
N% = 0: MaxDivisors% = 0: AntiPrimeCount% = 0
WHILE AntiPrimeCount% < MaxAntiPrime%
  N% = N% + 1
  Divisors% = DivisorCount(N%)
  IF Divisors% > MaxDivisors% THEN
    PRINT STR$(N%);
    MaxDivisors% = Divisors%
    AntiPrimeCount% = AntiPrimeCount% + 1
  END IF
WEND
PRINT
END

FUNCTION DivisorCount (V%)
  Total% = 1: N% = V%
  WHILE N% MOD 2 = 0
    Total% = Total% + 1
    N% = N% \ 2
  WEND
  P% = 3
  WHILE (P% * P%) <= N%
    Count% = 1
    WHILE N% MOD P% = 0
      Count% = Count% + 1
      N% = N% \ P%
    WEND
    P% = P% + 2
    Total% = Total% * Count%
  WEND
  IF N% > 1 THEN Total% = Total% * 2
  DivisorCount = Total%
END FUNCTION
Output:
 1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

Tiny BASIC[edit]

Works with: TinyBasic
100 LET A=0
101 LET N=1
102 LET H=0
103 PRINT "The first 20 anti-primes are:"
105 GOSUB 150
106 LET H=F
107 LET A=A+1
108 PRINT N
109 LET N=N+1
110 IF A<20 THEN GOTO 105
111 END
150 GOSUB 200
151 IF F>H THEN RETURN
152 LET N=N+1
153 GOTO 150
200 LET F=0
201 LET C=1
205 IF N/C*C=N THEN LET F=F+1
206 LET C=C+1
207 IF C<=N THEN GOTO 205
208 RETURN
Output:
The first 20 anti-primes are:
1
2
4
6
12
24
36
48
60
120
180
240
360
720
840
1260
1680
2520
5040
7560

VBA[edit]

Translation of: Phix
Private Function factors(n As Integer) As Collection
    Dim f As New Collection
    For i = 1 To Sqr(n)
        If n Mod i = 0 Then
            f.Add i
            If n / i <> i Then f.Add n / i
        End If
    Next i
    f.Add n
    Set factors = f
End Function
Public Sub anti_primes()
    Dim n As Integer, maxd As Integer
    Dim res As New Collection, lenght As Integer
    Dim lf As Integer
    n = 1: maxd = -1
    Length = 0
    Do While res.count < 20
        lf = factors(n).count
        If lf > maxd Then
            res.Add n
            maxd = lf
        End If
        n = n + IIf(n > 1, 2, 1)
    Loop
    Debug.Print "The first 20 anti-primes are:";
    For Each x In res
        Debug.Print x;
    Next x
End Sub
Output:
The first 20 anti-primes are: 1  2  4  6  12  24  36  48  60  120  180  240  360  720  840  1260  1680  2520  5040  7560 

Visual Basic .NET[edit]

Translation of: D
Module Module1

    Function CountDivisors(n As Integer) As Integer
        If n < 2 Then
            Return 1
        End If
        Dim count = 2 '1 and n
        For i = 2 To n \ 2
            If n Mod i = 0 Then
                count += 1
            End If
        Next
        Return count
    End Function

    Sub Main()
        Dim maxDiv, count As Integer
        Console.WriteLine("The first 20 anti-primes are:")

        Dim n = 1
        While count < 20
            Dim d = CountDivisors(n)

            If d > maxDiv Then
                Console.Write("{0} ", n)
                maxDiv = d
                count += 1
            End If
            n += 1
        End While

        Console.WriteLine()
    End Sub

End Module
Output:
The first 20 anti-primes are:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

Yabasic[edit]

This example does not show the output mentioned in the task description on this page (or a page linked to from here). Please ensure that it meets all task requirements and remove this message.
Note that phrases in task descriptions such as "print and display" and "print and show" for example, indicate that (reasonable length) output be a part of a language's solution.


Translation of: AWK
print "The first 20 anti-primes are:"

while (count < 20)
    n = n + 1
    d = count_divisors(n)
    if d > max_divisors then
        print n;
        max_divisors = d
        count = count + 1
    end if
wend
print

sub count_divisors(n)
    local count, i
    
    if n < 2 return 1
    
    count = 2
    for i = 2 to n/2
      if not(mod(n,  i)) count = count + 1
    next
    return count
end sub
Translation of: Lua
// First 20 antiprimes.
 
sub count_factors(number)
    local count, attempt
    
    for attempt = 1 to number
        if not mod(number, attempt) count = count + 1
    next
    return count
end sub
 
sub antiprimes$(goal)
    local factors, list$, number, mostFactors, nitems
    
    number = 1
    
    while nitems < goal
        factors = count_factors(number)
        if factors > mostFactors then
            list$ = list$ + ", " + str$(number)
            nitems = nitems + 1
            mostFactors = factors
        endif
        number = number + 1
    wend
    return list$
end sub

print "The first 20 antiprimes:"
print mid$(antiprimes$(20), 3)
print "Done."

BCPL[edit]

get "libhdr"
manifest $( LIMIT = 20 $)

let nfactors(n) =
    n < 2 -> 1, valof
$(  let c = 2
    for i=2 to n/2
        if n rem i = 0 then c := c + 1
    resultis c
$)

let start() be
$(  let max = 0 and seen = 0 and n = 1
    while seen < LIMIT
    $(  let f = nfactors(n)
        if f > max
        $(  writef("%N ",n)
            max := f
            seen := seen + 1
        $)
        n := n + 1
    $)
    wrch('*N')
$)
Output:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

C[edit]

Translation of: Go
#include <stdio.h>

int countDivisors(int n) {
    int i, count;
    if (n < 2) return 1;
    count = 2; // 1 and n
    for (i = 2; i <= n/2; ++i) {
        if (n%i == 0) ++count;
    }
    return count;
}

int main() {
    int n, d, maxDiv = 0, count = 0;
    printf("The first 20 anti-primes are:\n");
    for (n = 1; count < 20; ++n) {
        d = countDivisors(n); 
        if (d > maxDiv) {
            printf("%d ", n);
            maxDiv = d;
            count++;
        }
    }
    printf("\n"); 
    return 0;
}
Output:
The first 20 anti-primes are:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560 

C#[edit]

Works with: C sharp version 7
using System;
using System.Linq;
using System.Collections.Generic;
					
public static class Program
{
    public static void Main() =>
        Console.WriteLine(string.Join(" ", FindAntiPrimes().Take(20)));
	
    static IEnumerable<int> FindAntiPrimes() {
        int max = 0;
        for (int i = 1; ; i++) {
            int divisors = CountDivisors(i);
            if (divisors > max) {
                max = divisors;
                yield return i;
            }
        }
	
        int CountDivisors(int n) => Enumerable.Range(1, n / 2).Count(i => n % i == 0) + 1;
    }
}
Output:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

C++[edit]

Translation of: C
#include <iostream>

int countDivisors(int n) {
    if (n < 2) return 1;
    int count = 2; // 1 and n
    for (int i = 2; i <= n/2; ++i) {
        if (n%i == 0) ++count;
    }
    return count;
}

int main() {
    int maxDiv = 0, count = 0;
    std::cout << "The first 20 anti-primes are:" << std::endl;
    for (int n = 1; count < 20; ++n) {
        int d = countDivisors(n);
        if (d > maxDiv) {
            std::cout << n << " ";
            maxDiv = d;
            count++;
        }
    }
    std::cout << std::endl;
    return 0;
}
Output:
The first 20 anti-primes are:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560 

CLU[edit]

% Count factors
factors = proc (n: int) returns (int)
    if n<2 then return(1) end
    count: int := 2
    for i: int in int$from_to(2, n/2) do
        if n//i = 0 then count := count + 1 end
    end
    return(count)
end factors

% Generate antiprimes
antiprimes = iter () yields (int)
    max: int := 0
    n: int := 1
    while true do
        f: int := factors(n)
        if f > max then
            yield(n)
            max := f
        end
        n := n + 1
    end
end antiprimes

% Show the first 20 antiprimes
start_up = proc ()
    max = 20
    po: stream := stream$primary_output()
    count: int := 0
    
    for i: int in antiprimes() do
        stream$puts(po, int$unparse(i) || " ")
        count := count + 1
        if count = max then break end
    end
end start_up
Output:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

COBOL[edit]

      ******************************************************************
      * COBOL solution to Anti-primes challange
      * The program was run on OpenCobolIDE
      ******************************************************************
       IDENTIFICATION DIVISION.
       PROGRAM-ID. ANGLE-PRIMES.

       ENVIRONMENT DIVISION.
       DATA DIVISION.
       WORKING-STORAGE SECTION.
       77  ANTI-PRIMES-CTR              PIC 9(3) VALUE 0.
       77  FACTORS-CTR                  PIC 9(3) VALUE 0.
       77  WS-INTEGER                   PIC 9(5) VALUE 1.
       77  WS-MAX                       PIC 9(5) VALUE 0.
       77  WS-I                         PIc 9(5) VALUE 0.
       77  WS-LIMIT                     PIC 9(5) VALUE 1.
       77  WS-REMAINDER                 PIC 9(5).

       01  OUT-HDR         PIC X(23)    VALUE 'SEQ ANTI-PRIME FACTORS'.
       01  OUT-LINE.
           05 OUT-SEQ      PIC 9(3).
           05 FILLER       PIC X(3)     VALUE SPACES.
           05 OUT-ANTI     PIC ZZZZ9.
           05 FILLER       PIC X(4)     VALUE SPACES.
           05 OUT-FACTORS  PIC ZZZZ9.

       PROCEDURE DIVISION.
       000-MAIN.
           DISPLAY OUT-HDR.
           PERFORM 100-GET-ANTI-PRIMES
               VARYING WS-INTEGER FROM 1 By 1
               UNTIL ANTI-PRIMES-CTR >= 20.
           STOP RUN.

       100-GET-ANTI-PRIMES.
           SET FACTORS-CTR TO 0.
           COMPUTE WS-LIMIT = 1 + WS-INTEGER ** .5.
           PERFORM 200-COUNT-FACTORS
               VARYING WS-I FROM 1 BY 1
               UNTIL WS-I >= WS-LIMIT.
           IF FACTORS-CTR > WS-MAX
               ADD 1 TO ANTI-PRIMES-CTR
               COMPUTE WS-MAX = FACTORS-CTR
               MOVE ANTI-PRIMES-CTR TO OUT-SEQ
               MOVE WS-INTEGER TO OUT-ANTI
               MOVE FACTORS-CTR TO OUT-FACTORS
               DISPLAY OUT-LINE
           END-IF.

       200-COUNT-FACTORS.
           COMPUTE WS-REMAINDER =
               FUNCTION MOD(WS-INTEGER WS-I).
           IF WS-REMAINDER = ZERO
               ADD 1 TO FACTORS-CTR
               IF WS-INTEGER NOT = WS-I ** 2
                   ADD 1 TO FACTORS-CTR
               END-IF
           END-IF.

      ******************************************************************
      *    OUTPUT:
      ******************************************************************
      *     SEQ ANTI-PRIME FACTORS
      *     001       1        1
      *     002       2        2
      *     003       4        3
      *     004       6        4
      *     005      12        6
      *     006      24        8
      *     007      36        9
      *     008      48       10
      *     009      60       12
      *     010     120       16
      *     011     180       18
      *     012     240       20
      *     013     360       24
      *     014     720       30
      *     015     840       32
      *     016    1260       36
      *     017    1680       40
      *     018    2520       48
      *     019    5040       60
      *     020    7560       64
      ******************************************************************

Common Lisp[edit]

(defun factors (n &aux (lows '()) (highs '()))
    (do ((limit (1+ (isqrt n))) (factor 1 (1+ factor)))
        ((= factor limit)
            (when (= n (* limit limit))
                (push limit highs))
            (remove-duplicates (nreconc lows highs)))
        (multiple-value-bind (quotient remainder) (floor n factor)
            (when (zerop remainder)
                (push factor lows)
                (push quotient highs)))))

(defun anti-prime ()
    (format t "The first 20 anti-primes are :~%")
    (do ((dmax 0) (c 0) (i 0 (1+ i)))
        ((= c 20))
        (setf facts (list-length (factors i)))
        (when (< dmax facts)
            (format t "~d " i)
            (setq dmax facts)
            (incf c))))
Output:
The first 20 anti-primes are :
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

Cowgol[edit]

include "cowgol.coh";
const AMOUNT := 20;

sub countFactors(n: uint16): (count: uint16) is
    var i: uint16 := 1;
    count := 1;
    while i <= n/2 loop
        if n%i == 0 then
            count := count + 1;
        end if;
        i := i + 1;
    end loop;
end sub;

var max: uint16 := 0;
var seen: uint8 := 0;
var n: uint16 := 1;
var f: uint16 := 0;

while seen < AMOUNT loop;
    f := countFactors(n);
    if f > max then
        print_i16(n);
        print_char(' ');
        max := f;
        seen := seen + 1;
    end if;
    n := n + 1;
end loop;
print_nl();
Output:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

Crystal[edit]

Translation of: C++
def count_divisors(n : Int64) : Int64
  return 1_i64 if n < 2
  count = 2_i64

  i = 2
  while i <= n // 2
    count += 1 if n % i == 0
    i += 1
  end

  count
end

max_div = 0_i64
count = 0_i64

print "The first 20 anti-primes are: "

n = 1_i64
while count < 20
  d = count_divisors n

  if d > max_div
    print "#{n} "
    max_div = d
    count += 1
  end

  n += 1
end

puts ""
Output:
The first 20 anti-primes are: 1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

D[edit]

Translation of: C++
import std.stdio;

int countDivisors(int n) {
    if (n < 2) {
        return 1;
    }
    int count = 2; // 1 and n
    for (int i = 2; i <= n/2; ++i) {
        if (n % i == 0) {
            ++count;
        }
    }
    return count;
}

void main() {
    int maxDiv, count;
    writeln("The first 20 anti-primes are:");
    for (int n = 1; count < 20; ++n) {
        int d = countDivisors(n);
        if (d > maxDiv) {
            write(n, ' ');
            maxDiv = d;
            count++;
        }
    }
    writeln;
}
Output:
The first 20 anti-primes are:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

Delphi[edit]

See #Pascal.

Elixir[edit]

Translation of: Erlang
defmodule AntiPrimes do
	def divcount(n) when is_integer(n), do: divcount(n, 1, 0)

	def divcount(n, d, count) when d * d > n, do: count
	def divcount(n, d, count) do
		divs = case rem(n, d) do
			0 ->
				case n - d * d do
					0 -> 1
					_ -> 2
				end
			_ -> 0
		end
		divcount(n, d + 1, count + divs)
	end

	def antiprimes(n), do: antiprimes(n, 1, 0, [])

	def antiprimes(0, _, _, l), do: Enum.reverse(l)
	def antiprimes(n, m, max, l) do
		count = divcount(m)
		case count > max do
			true -> antiprimes(n-1, m+1, count, [m|l])
			false -> antiprimes(n, m+1, max, l)
		end
	end

	def main() do
		:io.format("The first 20 anti-primes are ~w~n", [antiprimes(20)])
	end
end
Output:
The first 20 anti-primes are [1,2,4,6,12,24,36,48,60,120,180,240,360,720,840,1260,1680,2520,5040,7560]

Erlang[edit]

divcount(N) -> divcount(N, 1, 0).

divcount(N, D, Count) when D*D > N -> Count;
divcount(N, D, Count) ->
    Divs = case N rem D of
        0 ->
            case N - D*D of
                0 -> 1;
                _ -> 2
            end;
        _ -> 0
    end,
    divcount(N, D + 1, Count + Divs).


antiprimes(N) -> antiprimes(N, 1, 0, []).

antiprimes(0, _, _, L) -> lists:reverse(L);
antiprimes(N, M, Max, L) ->
    Count = divcount(M),
    case Count > Max of
        true  -> antiprimes(N-1, M+1, Count, [M|L]);
        false -> antiprimes(N, M+1, Max, L)
    end.


main(_) ->
    io:format("The first 20 anti-primes are ~w~n", [antiprimes(20)]).
Output:
The first 20 anti-primes are [1,2,4,6,12,24,36,48,60,120,180,240,360,720,840,1260,1680,2520,5040,7560]

F#[edit]

The Function[edit]

This task uses Extensible Prime Generator (F#)

// Find Antı-Primes. Nigel Galloway: Secember 10th., 2018
let  N=200000000000000000000000000I
let fI,_=Seq.scan(fun (_,g) e->(e,e*g)) (2I,4I) (primes|>Seq.skip 1|>Seq.map bigint)|>Seq.takeWhile(fun(_,n)->n<N)|>List.ofSeq|>List.unzip
let fG g=Seq.unfold(fun ((n,i,e) as z)->Some(z,(n+1,i+1,(e*g)))) (1,2,g)|>Seq.takeWhile(fun(_,_,n)->n<N)
let fE n i=n|>Seq.collect(fun(n,e,g)->Seq.map(fun(a,c,b)->(a,c*e,g*b)) (i|>Seq.takeWhile(fun(g,_,_)->g<=n)) |> Seq.takeWhile(fun(_,_,n)->n<N))
let fL,_=Seq.concat(Seq.scan(fun n g->fE n (fG g)) (seq[(2147483647,1,1I)]) fI)|>List.ofSeq|>List.sortBy(fun(_,_,n)->n)|>List.fold(fun ((a,b) as z) (_,n,g)->if n>b then ((n,g)::a,n) else z) ([],0)

The Task[edit]

printfn "The first 20 anti-primes are :-"; for (_,g) in (List.rev fL)|>List.take 20 do printfn "%A" g
Output:
The first 20 anti-primes are :-
1
2
4
6
12
24
36
48
60
120
180
240
360
720
840
1260
1680
2520
5040
7560

Extra Credit[edit]

printfn "There are %d anti-primes less than %A:-" (List.length fL) N; for (n,g) in (List.rev fL) do printfn "%A has %d dividers" g n
Output:
There are 245 anti-primes less than 200000000000000000000000000:-
1 has 1 dividers
2 has 2 dividers
4 has 3 dividers
6 has 4 dividers
12 has 6 dividers
24 has 8 dividers
36 has 9 dividers
48 has 10 dividers
60 has 12 dividers
120 has 16 dividers
180 has 18 dividers
240 has 20 dividers
360 has 24 dividers
720 has 30 dividers
840 has 32 dividers
1260 has 36 dividers
1680 has 40 dividers
2520 has 48 dividers
5040 has 60 dividers
7560 has 64 dividers
10080 has 72 dividers
15120 has 80 dividers
20160 has 84 dividers
25200 has 90 dividers
27720 has 96 dividers
45360 has 100 dividers
50400 has 108 dividers
55440 has 120 dividers
83160 has 128 dividers
110880 has 144 dividers
166320 has 160 dividers
221760 has 168 dividers
277200 has 180 dividers
332640 has 192 dividers
498960 has 200 dividers
554400 has 216 dividers
665280 has 224 dividers
720720 has 240 dividers
1081080 has 256 dividers
1441440 has 288 dividers
2162160 has 320 dividers
2882880 has 336 dividers
3603600 has 360 dividers
4324320 has 384 dividers
6486480 has 400 dividers
7207200 has 432 dividers
8648640 has 448 dividers
10810800 has 480 dividers
14414400 has 504 dividers
17297280 has 512 dividers
21621600 has 576 dividers
32432400 has 600 dividers
36756720 has 640 dividers
43243200 has 672 dividers
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73513440 has 768 dividers
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367567200 has 1152 dividers
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48519593772249600 has 57600 dividers
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72779390658374400 has 62208 dividers
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106858629141264000 has 65536 dividers
112201560598327200 has 69120 dividers
149602080797769600 has 73728 dividers
224403121196654400 has 80640 dividers
299204161595539200 has 82944 dividers
374005201994424000 has 86016 dividers
448806242393308800 has 92160 dividers
673209363589963200 has 96768 dividers
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6133685312708553600 has 147456 dividers
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12267370625417107200 has 165888 dividers
15334213281771384000 has 172032 dividers
18401055938125660800 has 184320 dividers
27601583907188491200 has 193536 dividers
30668426563542768000 has 196608 dividers
36802111876251321600 has 207360 dividers
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55203167814376982400 has 221184 dividers
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368021118762513216000 has 307200 dividers
395622702669701707200 has 322560 dividers
527496936892935609600 has 331776 dividers
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148754136203807841907200 has 921600 dividers
185942670254759802384000 has 983040 dividers
223131204305711762860800 has 995328 dividers
278914005382139703576000 has 1032192 dividers
371885340509519604768000 has 1105920 dividers
557828010764279407152000 has 1179648 dividers
743770681019039209536000 has 1228800 dividers
818147749120943130489600 has 1244160 dividers
985496152350226952635200 has 1290240 dividers
1115656021528558814304000 has 1327104 dividers
1487541362038078419072000 has 1351680 dividers
1636295498241886260979200 has 1382400 dividers
1970992304700453905270400 has 1474560 dividers
2454443247362829391468800 has 1492992 dividers
2956488457050680857905600 has 1548288 dividers
3284987174500756508784000 has 1572864 dividers
3941984609400907810540800 has 1658880 dividers
4927480761751134763176000 has 1720320 dividers
5912976914101361715811200 has 1769472 dividers
7883969218801815621081600 has 1843200 dividers
9854961523502269526352000 has 1966080 dividers
11825953828202723431622400 has 1990656 dividers
14782442285253404289528000 has 2064384 dividers
19709923047004539052704000 has 2211840 dividers
29564884570506808579056000 has 2359296 dividers
39419846094009078105408000 has 2457600 dividers
43361830703409985915948800 has 2488320 dividers
54202288379262482394936000 has 2580480 dividers
59129769141013617158112000 has 2654208 dividers
78839692188018156210816000 has 2703360 dividers
86723661406819971831897600 has 2764800 dividers
108404576758524964789872000 has 2949120 dividers
130085492110229957747846400 has 2985984 dividers
162606865137787447184808000 has 3096576 dividers
193814243295544634018256000 has 3145728 dividers

Factor[edit]

USING: assocs formatting kernel locals make math
math.primes.factors sequences.extras ;
IN: rosetta-code.anti-primes

<PRIVATE

: count-divisors ( n -- m )
    dup 1 = [ group-factors values [ 1 + ] map-product ] unless ;

: (n-anti-primes) ( md n count -- ?md' n' ?count' )
    dup 0 >
    [| max-div! n count! |
        n count-divisors :> d
        d max-div > [ d max-div! n , count 1 - count! ] when
        max-div n dup 60 >= 20 1 ? + count (n-anti-primes)
    ] when ;

PRIVATE>

: n-anti-primes ( n -- seq )
    [ 0 1 ] dip [ (n-anti-primes) 3drop ] { } make ;

: anti-primes-demo ( -- )
    20 n-anti-primes "First 20 anti-primes:\n%[%d, %]\n" printf ;

MAIN: anti-primes-demo
Output:
First 20 anti-primes:
{ 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560 }

Forth[edit]

This task uses Factors of an Integer with vectored execution

include ./factors.fs

: max-count ( n1 n2 -- n f )
    \ n is max(n1, factor-count n2); if n is new maximum then f = true.
    \
    count-factors 2dup <
    if   nip true
    else drop false
    then ;

: .anti-primes ( n -- )
    0 1 rot  \ stack: max, candidate, count
    begin
        >r dup >r max-count
        if   r> dup . r> 1-
        else r> r>
        then swap 1+ swap
    dup 0= until drop 2drop ;

." The first 20 anti-primes are: " 20 .anti-primes cr
bye
Output:
The first 20 anti-primes are: 1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560 

Fortran[edit]

Translation of: C
program anti_primes
    use iso_fortran_env, only: output_unit
    implicit none

    integer :: n, d, maxDiv, pCount

    write(output_unit,*) "The first 20 anti-primes are:"
    n = 1
    maxDiv = 0
    pCount = 0
    do
        if (pCount >= 20) exit

        d = countDivisors(n)
        if (d > maxDiv) then
            write(output_unit,'(I0,x)', advance="no") n
            maxDiv = d
            pCount = pCount + 1
        end if
        n = n + 1
    end do
    write(output_unit,*)
contains
    pure function countDivisors(n)
        integer, intent(in) :: n
        integer             :: countDivisors
        integer             :: i

        countDivisors = 1
        if (n < 2) return
        countDivisors = 2
        do i = 2, n/2
            if (modulo(n, i) == 0) countDivisors = countDivisors + 1
        end do
    end function countDivisors
end program anti_primes
Output:
 The first 20 anti-primes are:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560 

Frink[edit]

smallest = 0
n = 1
results = new array
do
{
   len = length[allFactors[n]]
   if len > smallest
   {
      results.push[n]
      smallest = len
   }
   n = n + 1
} until length[results] == 20

println[join[" ", results]]
Output:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

Go[edit]

Simple brute force approach which is quick enough here.

package main

import "fmt"

func countDivisors(n int) int {
    if n < 2 {
        return 1
    }
    count := 2 // 1 and n
    for i := 2; i <= n/2; i++ {
        if n%i == 0 {
            count++
        }
    }
    return count
}

func main() {
    fmt.Println("The first 20 anti-primes are:")
    maxDiv := 0
    count := 0
    for n := 1; count < 20; n++ {
        d := countDivisors(n)
        if d > maxDiv {
            fmt.Printf("%d ", n)
            maxDiv = d
            count++
        }
    }
    fmt.Println()
}
Output:
The first 20 anti-primes are:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560 

Groovy[edit]

Solution (uses Factors of an integer function "factorize()"):

def getAntiPrimes(def limit = 10) {
    def antiPrimes = []
    def candidate = 1L
    def maxFactors = 0

    while (antiPrimes.size() < limit) {
        def factors = factorize(candidate)
        if (factors.size() > maxFactors) {
            maxFactors = factors.size()
            antiPrimes << candidate
        }
        candidate++
    }
    antiPrimes
}

Test:

println (getAntiPrimes(20))

Output:

[1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560]

Haskell[edit]

import Data.List (find, group)
import Data.Maybe (fromJust)

firstPrimeFactor :: Int -> Int
firstPrimeFactor n = head $ filter ((0 ==) . mod n) [2 .. n]

allPrimeFactors :: Int -> [Int]
allPrimeFactors 1 = []
allPrimeFactors n =
  let first = firstPrimeFactor n
  in first : allPrimeFactors (n `div` first)

factorCount :: Int -> Int
factorCount 1 = 1
factorCount n = product ((succ . length) <$> group (allPrimeFactors n))

divisorCount :: Int -> (Int, Int)
divisorCount = (,) <*> factorCount

hcnNext :: (Int, Int) -> (Int, Int)
hcnNext (num, factors) =
  fromJust $ find ((> factors) . snd) (divisorCount <$> [num ..])

hcnSequence :: [Int]
hcnSequence = fst <$> iterate hcnNext (1, 1)

main :: IO ()
main = print $ take 20 hcnSequence
Output:
[1,2,4,6,12,24,36,48,60,120,180,240,360,720,840,1260,1680,2520,5040,7560]

J[edit]

   NB. factor count is the product of the incremented powers of prime factors
   factor_count =: [: */ [: >: _&q:

   NB. N are the integers 1 to 10000
   NB. FC are the corresponding factor counts
   FC =: factor_count&> N=: >: i. 10000

   NB. take from the integers N{~
   NB. the indexes of truth   I.
   NB. the vector which doesn't equal itself when rotated by one position  (~: _1&|.)
   NB. where that vector is the maximum over all prefixes of the factor counts  >./\FC
   N{~I.(~: _1&|.)>./\FC
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

Java[edit]

Translation of: Go
public class Antiprime {

    static int countDivisors(int n) {
        if (n < 2) return 1;
        int count = 2; // 1 and n
        for (int i = 2; i <= n/2; ++i) {
            if (n%i == 0) ++count;
        }
        return count;
    }

    public static void main(String[] args) {
        int maxDiv = 0, count = 0;
        System.out.println("The first 20 anti-primes are:");
        for (int n = 1; count < 20; ++n) {
            int d = countDivisors(n);
            if (d > maxDiv) {
                System.out.printf("%d ", n);
                maxDiv = d;
                count++;
            }
        }
        System.out.println();
    }
}
Output:
The first 20 anti-primes are:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560 

JavaScript[edit]

function factors(n) {
  var factors = [];
  for (var i = 1; i <= n; i++) {
    if (n % i == 0) {
      factors.push(i);
    }
  }
  return factors;
}

function generateAntiprimes(n) {
  var antiprimes = [];
  var maxFactors = 0;
  for (var i = 1; antiprimes.length < n; i++) {
    var ifactors = factors(i);
    if (ifactors.length > maxFactors) {
      antiprimes.push(i);
      maxFactors = ifactors.length;
    }
  }
  return antiprimes;
}

function go() {
  var number = document.getElementById("n").value;
  document.body.removeChild(document.getElementById("result-list"));
  document.body.appendChild(showList(generateAntiprimes(number)));
}

function showList(array) {
  var list = document.createElement("ul");
  list.id = "result-list";
  for (var i = 0; i < array.length; i++) {
    var item = document.createElement("li");
    item.appendChild(document.createTextNode(array[i]));
    list.appendChild(item);
  }
  return list;
}

Html to test with some styling

<!DOCTYPE html>
<html lang="en">
  <head>
    <meta charset="UTF-8" />
    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
    <meta http-equiv="X-UA-Compatible" content="ie=edge" />
    <script src="antiprimes.js"></script>
    <title>Anti-Primes</title>
    <style>
      body {padding: 50px;width: 50%;box-shadow: 0 0 15px 0 rgba(0, 0, 0, 0.25);margin: 15px auto;font-family: "Gill Sans", "Gill Sans MT", Calibri, "Trebuchet MS", sans-serif;letter-spacing: 1px;}
      a {color: #00aadd;text-decoration: none;}
      input {width: 50px;text-align: center;}
      ul {list-style: none;padding: 0;margin: 0;width: 25%;margin: auto;border: 1px solid #aaa;}
      li {text-align: center;background-color: #eaeaea;}
      li:nth-child(even) {background: #fff;}
    </style>
  </head>
  <body onload="go()">
    <h1>Anti-Primes</h1>
    <div class="info">
      The <a href="https://youtu.be/2JM2oImb9Qg">anti-primes</a> (or
      <a href="https://en.wikipedia.org/wiki/Highly_composite_number">highly composite numbers</a>, sequence
      <a href="https://oeis.org/A002182">A002182</a> in the <a href="https://oeis.org/">OEIS</a>) are the natural numbers with more factors than any
      smaller than itself.
    </div>
    <p>Generate first <input id="n" type="text" placeholder="Enter the number" value="20" /> anti-primes. <button onclick="go()">Go</button></p>
    <ul id="result-list"></ul>
  </body>
</html>

jq[edit]

Works with: jq

Works with gojq, the Go implementation of jq

# Compute the number of divisors, without calling sqrt
def ndivisors:
  def sum(s): reduce s as $x (null; .+$x);
  if . == 1 then 1
  else . as $n
  | sum( label $out
         | range(1; $n) as $i
         | ($i * $i) as $i2
         | if $i2 > $n then break $out
           else if $i2 == $n
                then 1
                elif ($n % $i) == 0
                then 2
                else empty
                end
           end)
  end;

# Emit the antiprimes as a stream
def antiprimes:
  1,
  foreach range(2; infinite; 2) as $i ({maxfactors: 1};
    .emit = null
    | ($i | ndivisors) as $nfactors
    | if $nfactors > .maxfactors
      then .emit = $i
      | .maxfactors = $nfactors
      else .
      end;
      select(.emit).emit);
 
"The first 20 anti-primes are:", limit(20; antiprimes)
Output:
The first 20 anti-primes are:
1
2
4
6
12
24
36
48
60
120
180
240
360
720
840
1260
1680
2520
5040
7560

Julia[edit]

using Primes, Combinatorics

function antiprimes(N, maxn = 2000000)
    antip = [1]  # special case: 1 is antiprime
    count = 1
    maxfactors = 1
    for i in 2:2:maxn # antiprimes > 2 should be even
        lenfac = length(unique(sort(collect(combinations(factor(Vector, i)))))) + 1
        if lenfac > maxfactors
            push!(antip, i)
            if length(antip) >= N
                return antip
            end
            maxfactors = lenfac
        end
    end
    antip
end  

println("The first 20 anti-primes are:\n", antiprimes(20))
println("The first 40 anti-primes are:\n", antiprimes(40))
Output:

The first 20 anti-primes are:
[1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560]
The first 40 anti-primes are:
[1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560, 
10080, 15120, 20160, 25200, 27720, 45360, 50400, 55440, 83160, 110880, 166320, 221760, 277200, 
332640, 498960, 554400, 665280, 720720, 1081080, 1441440]

Kotlin[edit]

Translation of: Go
// Version 1.3.10

fun countDivisors(n: Int): Int {
    if (n < 2) return 1;
    var count = 2 // 1 and n
    for (i in 2..n / 2) {
        if (n % i == 0) count++
    }
    return count;
}

fun main(args: Array<String>) {
    println("The first 20 anti-primes are:")
    var maxDiv = 0
    var count = 0
    var n = 1
    while (count < 20) {
        val d = countDivisors(n)
        if (d > maxDiv) {
            print("$n ")
            maxDiv = d
            count++
        }
        n++
    }
    println()
}
Output:
The first 20 anti-primes are:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560 

Lua[edit]

-- First 20 antiprimes.

function count_factors(number)
	local count = 0
	for attempt = 1, number do
		local remainder = number % attempt
		if remainder == 0 then
			count = count + 1
		end
	end
	return count
end

function antiprimes(goal)
	local list, number, mostFactors = {}, 1, 0
	while #list < goal do
		local factors = count_factors(number)
		if factors > mostFactors then
			table.insert(list, number)
			mostFactors = factors
		end
		number = number + 1
	end
	return list
end

function recite(list)
	for index, item in ipairs(list) do
		print(item)
	end
end

print("The first 20 antiprimes:")
recite(antiprimes(20))
print("Done.")
Output:
The first 20 antiprimes:
1
2
4
6
12
24
36
48
60
120
180
240
360
720
840
1260
1680
2520
5040
7560
Done.

Maple[edit]

antiprimes := proc(n)
local ap, i, max_divisors, num_divisors;
max_divisors := 0;
ap := [];

for i from 1 while numelems(ap) < n do
    num_divisors := numelems(NumberTheory:-Divisors(i));
    if num_divisors > max_divisors then
       ap := [op(ap), i];
       max_divisors := num_divisors;
    end if;
end do;

return ap;
end proc:
antiprimes(20);
Output:
[1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560]

Mathematica / Wolfram Language[edit]

sigma = DivisorSigma[0, #] &;
currentmax = -\[Infinity];
res = {};
Do[
 s = sigma[v];
 If[s > currentmax,
  AppendTo[res, v];
  currentmax = s;
  ];
 If[Length[res] >= 25, Break[]]
 ,
 {v, \[Infinity]}
 ]
res
Output:
{1,2,4,6,12,24,36,48,60,120,180,240,360,720,840,1260,1680,2520,5040,7560,10080,15120,20160,25200,27720}

Modula-2[edit]

MODULE Antiprimes;
FROM InOut IMPORT WriteCard, WriteLn;

CONST Amount = 20;
VAR max, seen, n, f: CARDINAL;

PROCEDURE factors(n: CARDINAL): CARDINAL;
    VAR facs, div: CARDINAL;
BEGIN
    IF n<2 THEN RETURN 1; END;
    facs := 2;
    FOR div := 2 TO n DIV 2 DO
        IF n MOD div = 0 THEN
            INC(facs);
        END;
    END;
    RETURN facs;
END factors;

BEGIN
    max := 0;
    seen := 0;
    n := 1;
    WHILE seen < Amount DO
        f := factors(n);
        IF f > max THEN
            WriteCard(n,5);
            max := f;
            INC(seen);
            IF seen MOD 10 = 0 THEN WriteLn(); END;
        END;
        INC(n);
    END;
END Antiprimes.
Output:
    1    2    4    6   12   24   36   48   60  120
  180  240  360  720  840 1260 1680 2520 5040 7560

Modula-3[edit]

Translation of: Modula-2
MODULE AntiPrimes EXPORTS Main;

IMPORT IO,Fmt;

CONST
  Amount = 20;
  
VAR
  Max,Seen,N,F:CARDINAL;

PROCEDURE Factors(N:CARDINAL):CARDINAL = 
  VAR
    Facts:CARDINAL;
  BEGIN
    IF N < 2 THEN RETURN 1 END;
    Facts := 2;
    FOR Div := 2 TO N DIV 2 DO
      IF N MOD Div = 0 THEN INC(Facts) END;
    END;
    RETURN Facts;
  END Factors;
  
BEGIN
  Max := 0;
  Seen := 0;
  N := 1;
  WHILE Seen < Amount DO
    F := Factors(N);
    IF F > Max THEN
      IO.Put(Fmt.F("%5s",Fmt.Int(N)));
      Max := F;
      INC(Seen);
      IF Seen MOD 10 = 0 THEN IO.Put("\n") END;
    END;
    INC(N);
  END;
END AntiPrimes.
Output:
    1    2    4    6   12   24   36   48   60  120
  180  240  360  720  840 1260 1680 2520 5040 7560

Nanoquery[edit]

Translation of: C
def countDivisors(n)
	if (n < 2)
		return 1
	end
	count = 2
	for i in range(2, int(n/2))
		if (n % i) = 0
			count += 1
		end
	end
	return count
end

maxDiv = 0
count = 0
println "The first 20 anti-primes are:"

for (n = 1) (count < 20) (n += 1)
	d = countDivisors(n)
	if d > maxDiv
		print format("%d ", n)
		maxDiv = d
		count += 1
	end
end
println
Output:
The first 20 anti-primes are:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560 

Nim[edit]

# First 20 antiprimes

proc countDivisors(n: int): int =
    if n < 2:
        return 1
    var count = 2
    for i in countup(2, (n / 2).toInt()):
        if n %% i == 0:
            count += 1
    return count

proc antiPrimes(n: int) = 
    echo("The first ", n, " anti-primes:")
    var maxDiv = 0
    var count = 0
    var i = 1
    while count < n:
        let d = countDivisors(i)
        if d > maxDiv:
            echo(i)
            maxDiv = d
            count += 1
        i += 1

antiPrimes(20)
Output:
The first 20 anti-primes:
1
2
4
6
12
24
36
48
60
120
180
240
360
720
840
1260
1680
2520
5040
7560

Oberon-2[edit]

Translation of: Modula-2
MODULE AntiPrimes;

  IMPORT Out;
    
  CONST
    Amount = 20;
    
  VAR
    Max,Seen,N,F:INTEGER;

  PROCEDURE Factors(N:INTEGER):INTEGER;
    VAR
      Facts,Div:INTEGER;
  BEGIN
    IF N < 2 THEN RETURN 1 END;
    Facts := 2;
    FOR Div := 2 TO N DIV 2 DO
      IF N MOD Div = 0 THEN INC(Facts) END;
    END;
    RETURN Facts;
  END Factors;
  
BEGIN
  Max := 0;
  Seen := 0;
  N := 1;
  WHILE Seen < Amount DO
    F := Factors(N);
    IF F > Max THEN
      Out.Int(N,5);
      Max := F;
      INC(Seen);
      IF Seen MOD 10 = 0 THEN Out.Ln END;
    END;
    INC(N);
  END;
END AntiPrimes.
Output:
    1    2    4    6   12   24   36   48   60  120
  180  240  360  720  840 1260 1680 2520 5040 7560

Objeck[edit]

Translation of: Java
class AntiPrimes {
  function : Main(args : String[]) ~ Nil {
    maxDiv := 0; count := 0;
    "The first 20 anti-primes are:"->PrintLine();
    for(n := 1; count < 20; ++n;) {
      d := CountDivisors(n);
      if(d > maxDiv) {
        "{$n} "->Print();
        maxDiv := d;
        count++;
      };
    };
    '\n'->Print();
  }

  function : native : CountDivisors(n : Int) ~ Int {
    if (n < 2) { return 1; };
    count := 2;
    for(i := 2; i <= n/2; ++i;) {
      if(n%i = 0) { ++count; };
    };
    return count;
  }
}
Output:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

Pascal[edit]

Easy factoring without primes.Decided to show count of factors.

program AntiPrimes;
{$IFdef FPC}
  {$MOde Delphi}
{$IFEND}
function getFactorCnt(n:NativeUint):NativeUint;
var
  divi,quot,pot,lmt : NativeUint;
begin
  result := 1;
  divi  := 1;
  lmt := trunc(sqrt(n));
  while divi < n do
  Begin
    inc(divi);
    pot := 0;
    repeat
      quot := n div divi;
      if n <> quot*divi then
        BREAK;
      n := quot;
      inc(pot);
    until false;
    result := result*(1+pot);
    //IF n= prime leave now
    if divi > lmt then
      BREAK;
  end;
end;

var
  i,Count,FacCnt,lastCnt: NativeUint;
begin
  count := 0;
  lastCnt := 0;
  i := 1;
  repeat
    FacCnt := getFactorCnt(i);
    if  lastCnt < FacCnt then
    Begin
      write(i,'(',FacCnt,'),');
      lastCnt:= FacCnt;
      inc(Count);
      if count = 12 then
        Writeln;
    end;
    inc(i);
  until Count >= 20;
  writeln;
end.
;Output:
1(1),2(2),4(3),6(4),12(6),24(8),36(9),48(10),60(12),120(16),180(18),240(20),
360(24),720(30),840(32),1260(36),1680(40),2520(48),5040(60),7560(64)

PARI/GP[edit]

countfactors(n)={
    my(count(m)= prod(i=1,#factor(m)~,factor(m)[i,2]+1));
    v=vector(n); 
    v[1]=1;
    for(x=2,n,
        v[x]=v[x-1]+1;
        while(count(v[x-1])>=count(v[x]),v[x]++));
return(v)}
countfactors(20)

Perl[edit]

Library: ntheory
use ntheory qw(divisors);

my @anti_primes;

for (my ($k, $m) = (1, 0) ; @anti_primes < 20 ; ++$k) {
    my $sigma0 = divisors($k);

    if ($sigma0 > $m) {
        $m = $sigma0;
        push @anti_primes, $k;
    }
}

printf("%s\n", join(' ', @anti_primes));
Output:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

Phix[edit]

with javascript_semantics
integer n=1, maxd = -1
sequence res = {}
while length(res)<20 do
    integer lf = length(factors(n,1))
    if lf>maxd then
        res &= n
        maxd = lf
    end if
    n += iff(n>1?2:1)
end while
printf(1,"The first 20 anti-primes are: %V\n",{res})
Output:
The first 20 anti-primes are: {1,2,4,6,12,24,36,48,60,120,180,240,360,720,840,1260,1680,2520,5040,7560}

Phixmonti[edit]

0 var count
0 var n
0 var max_divisors

"The first 20 anti-primes are:" print nl

def count_divisors
    dup 2 < if
        drop
        1
    else
        2
        swap 1 over 2 / 2 tolist
        for
            over swap mod not if swap 1 + swap endif
        endfor
        drop
    endif
enddef

true 
while
    count 20 < dup if
        n 1 + var n
        n count_divisors
        dup max_divisors > if
            n print " " print
            var max_divisors
            count 1 + var count
        else
            drop
        endif
    endif
endwhile

nl
msec print

Picat[edit]

Translation of: Go
Works with: Picat
count_divisors(1) = 1.

count_divisors(N) = Count, N >= 2 =>
    Count = 2,
    foreach (I in 2..N/2)
        if (N mod I == 0) then
            Count := Count + 1
        end
    end.

main =>
    println("The first 20 anti-primes are:"),
    MaxDiv = 0,
    Count = 0,
    N = 1,
    while (Count < 20)
        D := count_divisors(N),
        if (D > MaxDiv) then
            printf("%d ", N),
            MaxDiv := D,
            Count := Count + 1
        end,
        N := N + 1
    end,
    nl.
Output:
The first 20 anti-primes are:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

PicoLisp[edit]

(de factors (N)
   (let C 1
      (when (>= N 2)
         (inc 'C)
         (for (I 2 (>= (/ N 2) I) (inc I))
            (and (=0 (% N I)) (inc 'C)) ) )
      C ) )
(de anti (X)
   (let (M 0  I 0  N 0)
      (make
         (while (> X I)
            (inc 'N)
            (let R (factors N)
               (when (> R M)
                  (link N)
                  (setq M R)
                  (inc 'I) ) ) ) ) ) )
(println (anti 20))
Output:
(1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560)

PILOT[edit]

C :n=1
  :max=0
  :seen=0
  
*number
U :*count
T (c>max):#n
C (c>max):seen=seen+1
C (c>max):max=c
  :n=n+1
J (seen<20):*number
E :

*count
C (n=1):c=1
E (n=1):
C :c=2
  :i=2
*cnloop
E (i>n/2):
C (i*(n/i)=n):c=c+1
  :i=i+1
J :*cnloop
Output:
1
2
4
6
12
24
36
48
60
120
180
240
360
720
840
1260
1680
2520
5040
7560

PL/I[edit]

antiprimes: procedure options(main);

    /* count the factors of a number */
    countFactors: procedure(n) returns(fixed);
        declare (n, i, count) fixed;
        if n<2 then return(1);
        count = 1;
        do i=1 to n/2;
            if mod(n,i) = 0 then count = count + 1;
        end;
        return(count);
    end countFactors;
    
    declare maxFactors fixed static init (0);
    declare seen fixed static init (0);
    declare n fixed;
    declare factors fixed;
    
    do n=1 repeat(n+1) while(seen < 20);
        factors = countFactors(n);
        if factors > maxFactors then do;
            put edit(n) (F(5));
            maxFactors = factors;
            seen = seen + 1;
            if mod(seen,15) = 0 then put skip;
        end;
    end;
end antiprimes;
Output:
    1    2    4    6   12   24   36   48   60  120  180  240  360  720  840
 1260 1680 2520 5040 7560

PL/M[edit]

100H:
/* CP/M CALLS */
BDOS: PROCEDURE (FN, ARG); DECLARE FN BYTE, ARG ADDRESS; GO TO 5; END BDOS;
EXIT: PROCEDURE; CALL BDOS(0,0); END EXIT;
PRINT: PROCEDURE (S); DECLARE S ADDRESS; CALL BDOS(9,S); END PRINT;

/* PRINT A NUMBER */
PRINT$NUMBER: PROCEDURE (N);
    DECLARE S (7) BYTE INITIAL ('..... $');
    DECLARE (N, P) ADDRESS, C BASED P BYTE;
    P = .S(5);
DIGIT:
    P = P - 1;
    C = N MOD 10 + '0';
    N = N / 10;
    IF N > 0 THEN GO TO DIGIT;
    CALL PRINT(P);
END PRINT$NUMBER;

/* COUNT THE FACTORS OF A NUMBER */
COUNT$FACTORS: PROCEDURE (N) ADDRESS;
    DECLARE (N, I, COUNT) ADDRESS;
    IF N<2 THEN RETURN 1;
    COUNT = 1;
    DO I=1 TO N/2;
        IF N MOD I = 0 THEN COUNT = COUNT + 1;
    END;
    RETURN COUNT;
END COUNT$FACTORS;

DECLARE MAX$FACTORS ADDRESS INITIAL (0);
DECLARE SEEN BYTE INITIAL (0);
DECLARE N ADDRESS INITIAL (1);
DECLARE FACTORS ADDRESS;

DO WHILE SEEN < 20;
    FACTORS = COUNT$FACTORS(N);
    IF FACTORS > MAX$FACTORS THEN DO;
        CALL PRINT$NUMBER(N);
        MAX$FACTORS = FACTORS;
        SEEN = SEEN + 1;
    END;
    N = N + 1;
END;
CALL EXIT;
EOF
Output:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

Processing[edit]

void setup() {
  int most_factors = 0;
  IntList anti_primes = new IntList();
  int n = 1;
  while (anti_primes.size() < 20) {
    int counter = 1;
    for (int i = 1; i <= n / 2; i++) {
      if (n % i == 0) {
        counter++;
      }
    }
    if (counter > most_factors) {
      anti_primes.append(n);
      most_factors = counter;
    }
    n++;
  }
  for (int num : anti_primes) {
    print(num + " ");
  }
}
Output:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

Prolog[edit]

Translation of: Erlang
divcount(N, Count) :- divcount(N, 1, 0, Count).

divcount(N, D, C, C) :- D*D > N, !.
divcount(N, D, C, Count) :-
    succ(D, D2),
    divs(N, D, A), plus(A, C, C2),
    divcount(N, D2, C2, Count).

divs(N, D, 0) :- N mod D =\= 0, !.
divs(N, D, 1) :- D*D =:= N, !.
divs(_, _, 2).


antiprimes(N, L) :- antiprimes(N, 1, 0, [], L).

antiprimes(0, _, _, L, R) :- reverse(L, R), !.
antiprimes(N, M, Max, L, R) :-
    divcount(M, Count),
    succ(M, M2),
    (Count > Max
        -> succ(N0, N), antiprimes(N0, M2, Count, [M|L], R)
         ; antiprimes(N, M2, Max, L, R)).

main :-
    antiprimes(20, X),
    write("The first twenty anti-primes are "), write(X), nl,
    halt.

?- main.
Output:
The first twenty anti-primes are [1,2,4,6,12,24,36,48,60,120,180,240,360,720,840,1260,1680,2520,5040,7560]

Python[edit]

Uses the fast prime function from Factors of an integer#Python

from itertools import chain, count, cycle, islice, accumulate
 
def factors(n):
    def prime_powers(n):
        for c in accumulate(chain([2, 1, 2], cycle([2,4]))):
            if c*c > n: break
            if n%c: continue
            d,p = (), c
            while not n%c:
                n,p,d = n//c, p*c, d+(p,)
            yield d
        if n > 1: yield n,
 
    r = [1]
    for e in prime_powers(n):
        r += [a*b for a in r for b in e]
    return r
    
def antiprimes():
    mx = 0
    yield 1
    for c in count(2,2):
        if c >= 58: break
        ln = len(factors(c))
        if ln > mx:
            yield c
            mx = ln
    for c in count(60,30):
        ln = len(factors(c))
        if ln > mx:
            yield c
            mx = ln  

if __name__ == '__main__':
    print(*islice(antiprimes(), 40)))
Output:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560 10080 15120 20160 25200 27720 45360 50400 55440 83160 110880 166320 221760 277200 332640 498960 554400 665280 720720 1081080 1441440
old algorithm (without count(60,30) part) time to find first 40 antiprimes: around 14 seconds
new algorithm (with count(60,30) part) time to find first 40 antiprimes: around 0.4 seconds

Quackery[edit]

factors is defined at Factors of an integer.

  0 temp put
  [] 0
  [ 1+ dup factors size
    dup temp share > iff
      [ temp replace
        dup dip join ]
    else drop
    over size 20 = until ] 
  temp release 
  drop echo
Output:
[ 1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560 ]

R[edit]

Uses brute force. My first entry!

# Antiprimes

max_divisors <- 0

findFactors <- function(x){
  myseq <- seq(x)
  myseq[(x %% myseq) == 0]
}

antiprimes <- vector()
x <- 1
n <- 1
while(length(antiprimes) < 20){
  y <- findFactors(x)
  if (length(y) > max_divisors){
    antiprimes <- c(antiprimes, x)
    max_divisors <- length(y)
    n <- n + 1
  }
  x <- x + 1
}

antiprimes
Output:
 [1]    1    2    4    6   12   24   36   48   60  120  180  240  360  720  840 1260 1680 2520 5040 7560

Racket[edit]

#lang racket

(require racket/generator
         math/number-theory)

(define (get-divisors n)
  (apply * (map (λ (factor) (add1 (second factor))) (factorize n))))

(define antiprimes
  (in-generator
   (for/fold ([prev 0]) ([i (in-naturals 1)])
     (define divisors (get-divisors i))
     (when (> divisors prev) (yield i))
     (max prev divisors))))

(for/list ([i (in-range 20)] [antiprime antiprimes]) antiprime)
Output:
'(1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560)

Raku[edit]

(formerly Perl 6)

Works with: Rakudo version 2018.11

At its heart, this task is almost exactly the same as Proper_Divisors, it is just asking for slightly different results. Much of this code is lifted straight from there.

Implemented as an auto-extending lazy list. Displaying the count of anti-primes less than 5e5 also because... why not.

sub propdiv (\x) {
    my @l = 1 if x > 1;
    (2 .. x.sqrt.floor).map: -> \d {
        unless x % d { @l.push: d; my \y = x div d; @l.push: y if y != d }
    }
    @l
}

my $last = 0;

my @anti-primes = lazy 1, |(|(2..59), 60, *+60 … *).grep: -> $c {
    my \mx = +propdiv($c);
    next if mx <= $last;
    $last = mx;
    $c
}

my $upto = 5e5;

put "First 20 anti-primes:\n{ @anti-primes[^20] }";

put "\nCount of anti-primes <= $upto: {+@anti-primes[^(@anti-primes.first: * > $upto, :k)]}";
Output:
First 20 anti-primes:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

Count of anti-primes <= 500000: 35

Red[edit]

Red []
inc: func ['v] [set v 1 + get v]    ;; shortcut function for n: n + 1

n: 0  found: 0 max_div: 0
print "the first 20 anti-primes are:"
while  [ inc n] [
 nDiv: 1      ;; count n / n extra
 if n > 1 [ repeat div n / 2 [ if n % div = 0  [inc nDiv] ] ]
 if nDiv > max_div [
    max_div: nDiv
    prin [n ""] 
    if 20 <= inc found [halt]
 ]
]
Output:

the first 20 anti-primes are: 1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560 (halted)

REXX[edit]

even and odd numbers[edit]

This REXX version is using a modified version of a highly optimized   proper divisors   function.

Programming note:   although the solution to this Rosetta Code task is trivial, a fair amount of optimization was incorporated into the REXX program to find larger anti─primes (also known as   highly─composite numbers).

The   #DIVS   function could be further optimized by only processing   even   numbers, with unity being treated as a special case.

/*REXX program finds and displays  N  number of anti─primes or highly─composite numbers.*/
parse arg N .                                    /*obtain optional argument from the CL.*/
if N=='' | N==","  then N= 20                    /*Not specified?  Then use the default.*/
maxD= 0                                          /*the maximum number of divisors so far*/
say '─index─ ──anti─prime──'                     /*display a title for the numbers shown*/
#= 0                                             /*the count of anti─primes found  "  " */
     do once=1  for 1
        do i=1  for 59                           /*step through possible numbers by twos*/
        d= #divs(i);  if d<=maxD  then iterate   /*get # divisors;  Is too small?  Skip.*/
        #= # + 1;     maxD= d                    /*found an anti─prime #;  set new minD.*/
        say center(#, 7)  right(i, 10)           /*display the index and the anti─prime.*/
        if #>=N  then leave once                 /*if we have enough anti─primes, done. */
        end   /*i*/

        do j=60  by 20                           /*step through possible numbers by 20. */
        d= #divs(j);  if d<=maxD  then iterate   /*get # divisors;  Is too small?  Skip.*/
        #= # + 1;     maxD= d                    /*found an anti─prime #;  set new minD.*/
        say center(#, 7)  right(j, 10)           /*display the index and the anti─prime.*/
        if #>=N  then leave                      /*if we have enough anti─primes, done. */
        end   /*j*/
     end      /*once*/
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
#divs: procedure; parse arg x 1 y                /*X and Y:  both set from 1st argument.*/
       if x<3   then return x                    /*handle special cases for one and two.*/
       if x==4  then return 3                    /*   "      "      "    " four.        */
       if x<6   then return 2                    /*   "      "      "    " three or five*/
       odd= x // 2                               /*check if   X   is  odd  or not.      */
       if odd  then      #= 1                    /*Odd?   Assume  Pdivisors  count of 1.*/
               else do;  #= 3;     y= x % 2      /*Even?     "        "        "    " 3.*/
                    end                          /* [↑]   start with known num of Pdivs.*/

                  do k=3  for x%2-3  by 1+odd  while k<y  /*for odd numbers, skip evens.*/
                  if x//k==0  then do;  #= # + 2 /*if no remainder, then found a divisor*/
                                        y= x % k /*bump  #  Pdivs,  calculate limit  Y. */
                                        if k>=y  then do; #= # - 1; leave; end  /*limit?*/
                                   end                         /*                   ___ */
                              else if k*k>x  then leave        /*only divide up to √ x  */
                  end   /*k*/                    /* [↑]  this form of DO loop is faster.*/
       return #+1                                /*bump "proper divisors" to "divisors".*/
output   when using the default input of:     20
─index─ ──anti─prime──
   1             1
   2             2
   3             4
   4             6
   5            12
   6            24
   7            36
   8            48
   9            60
  10           120
  11           180
  12           240
  13           360
  14           720
  15           840
  16          1260
  17          1680
  18          2520
  19          5040
  20          7560
output   when using the default input of:     55
─index─ ──anti─prime──
   1             1
   2             2
   3             4
   4             6
   5            12
   6            24
   7            36
   8            48
   9            60
  10           120
  11           180
  12           240
  13           360
  14           720
  15           840
  16          1260
  17          1680
  18          2520
  19          5040
  20          7560
  21         10080
  22         15120
  23         20160
  24         25200
  25         27720
  26         45360
  27         50400
  28         55440
  29         83160
  30        110880
  31        166320
  32        221760
  33        277200
  34        332640
  35        498960
  36        554400
  37        665280
  38        720720
  39       1081080
  40       1441440
  41       2162160
  42       2882880
  43       3603600
  44       4324320
  45       6486480
  46       7207200
  47       8648640
  48      10810800
  49      14414400
  50      17297280
  51      21621600
  52      32432400
  53      36756720
  54      43243200
  55      61261200 

only even numbers[edit]

This REXX version only processes   even   numbers   (unity is treated as a special case.)

It's about   17%   faster than the 1st REXX version.

/*REXX program finds and displays  N  number of anti─primes or highly─composite numbers.*/
parse arg N .                                    /*obtain optional argument from the CL.*/
if N=='' | N==","  then N= 20                    /*Not specified?  Then use the default.*/
         @.= .;    @.1= 1;     @.2= 2;     @.4= 3;     @.5= 2;     @.6= 4
say '─index─ ──anti─prime──'                     /*display a title for the numbers shown*/
#= 1                                             /*the count of anti─primes found  "  " */
maxD= 1                                          /*the maximum number of divisors so far*/
say center(#, 7)  right(1, 10)                   /*display the index and the anti─prime.*/
     do once=1  for 1
        do i=2  by  2  to 59                     /*step through possible numbers by twos*/
        d= #divs(i);  if d<=maxD  then iterate   /*get # divisors;  Is too small?  Skip.*/
        #= # + 1;     maxD= d                    /*found an anti─prime #;  set new minD.*/
        say center(#, 7)  right(i, 10)           /*display the index and the anti─prime.*/
        if #>=N  then leave once                 /*if we have enough anti─primes, done. */
        end   /*i*/

        do j=60  by 20                           /*step through possible numbers by 20. */
        d= #divs(j);  if d<=maxD  then iterate   /*get # divisors;  Is too small?  Skip.*/
        #= # + 1;     maxD= d                    /*found an anti─prime #;  set new minD.*/
        say center(#, 7)  right(j, 10)           /*display the index and the anti─prime.*/
        if #>=N  then leave once                 /*if we have enough anti─primes, done. */
        L= length(j)                             /*obtain the length of the index  (J). */
        if L>3  then j= j + left(4, L-2, 0) - 20 /*Length>3?  Then calculate a long jump*/
        end   /*j*/
     end      /*once*/
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
#divs: parse arg x;  if @.x\==.  then return @.x /*if pre─computed, then return shortcut*/
       $= 3;     y= x % 2
                                                 /* [↑]   start with known num of Pdivs.*/
                  do k=3  for x%2-3  while k<y
                  if x//k==0  then do;  $= $ + 2 /*if no remainder, then found a divisor*/
                                        y= x % k /*bump  $  Pdivs,  calculate limit  Y. */
                                        if k>=y  then do; $= $ - 1; leave; end  /*limit?*/
                                   end                         /*                   ___ */
                              else if k*k>x  then leave        /*only divide up to √ x  */
                  end   /*k*/                    /* [↑]  this form of DO loop is faster.*/
       return $+1                                /*bump "proper divisors" to "divisors".*/
output   is identical to the 1st REXX version.


Ring[edit]

# Project : Anti-primes

see "working..." + nl
see "wait for done..." + nl + nl
see "the first 20 anti-primes are:" + nl + nl
maxDivisor = 0
num = 0
n = 0
result = list(20)
while num < 20
      n = n + 1
      div = factors(n)
      if (div > maxDivisor)
         maxDivisor = div
         num = num + 1
         result[num] = n
      ok
end
see "["
for n = 1 to len(result)
    if n < len(result)
       see string(result[n]) + ","
    else
       see string(result[n]) + "]" + nl + nl
    ok
next
see "done..." + nl

func factors(an)
     ansum = 2
     if an < 2
        return(1)
     ok
     for nr = 2 to an/2
         if an%nr = 0
            ansum = ansum+1
         ok
     next
     return ansum
Output:
working...
wait for done...

the first 20 anti-primes are:

[1,2,4,6,12,24,36,48,60,120,180,240,360,720,840,1260,1680,2520,5040,7560]

done...

Ruby[edit]

require 'prime'

def num_divisors(n)
  n.prime_division.inject(1){|prod, (_p,n)| prod *= (n + 1) } 
end

anti_primes = Enumerator.new do |y| # y is the yielder
  max = 0
  y << 1                            # yield 1
  2.step(nil,2) do |candidate|      # nil is taken as Infinity
     num = num_divisors(candidate)
     if  num > max
       y << candidate               # yield the candidate
       max = num
     end
  end
end

puts anti_primes.take(20).join(" ")
Output:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

Rust[edit]

Translation of: Go
fn count_divisors(n: u64) -> usize {
    if n < 2 {
        return 1;
    }
    2 + (2..=(n / 2)).filter(|i| n % i == 0).count()
}

fn main() {
    println!("The first 20 anti-primes are:");
    (1..)
        .scan(0, |max, n| {
            let d = count_divisors(n);
            Some(if d > *max {
                *max = d;
                Some(n)
            } else {
                None
            })
        })
        .flatten()
        .take(20)
        .for_each(|n| print!("{} ", n));
    println!();
}
Output:
The first 20 anti-primes are:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560 

Scala[edit]

This program uses an iterator to count the factors of a number, then builds a lazily evaluated list of all anti-primes. Finding the first 20 anti-primes involves merely taking the first 20 elements of the list.

def factorCount(num: Int): Int = Iterator.range(1, num/2 + 1).count(num%_ == 0) + 1
def antiPrimes: LazyList[Int] = LazyList.iterate((1: Int, 1: Int)){case (n, facs) => Iterator.from(n + 1).map(i => (i, factorCount(i))).dropWhile(_._2 <= facs).next}.map(_._1)
Output:
scala> print(antiPrimes.take(20).mkString(", "))
1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560

Seed7[edit]

$ include "seed7_05.s7i";

const func integer: countDivisors (in integer: number) is func
  result
    var integer: count is 1;
  local
    var integer: num is 0;
  begin
    for num range 1 to number div 2 do
      if number rem num = 0 then
        incr(count);
      end if;
    end for;
  end func;

const proc: main is func
  local
    var integer: maxDiv is 0;
    var integer: count is 0;
    var integer: number is 1;
    var integer: divisors is 1;
  begin
    writeln("The first 20 anti-primes are:");
    while count < 20 do
      divisors := countDivisors(number);
      if divisors > maxDiv then
        write(number <& " ");
        maxDiv := divisors;
        incr(count);
      end if;
      incr(number);
    end while;
    writeln;
  end func;
Output:
The first 20 anti-primes are:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560 

Sidef[edit]

Using the built-in Number.sigma0 method to count the number of divisors.

say with (0) {|max|
    1..Inf -> lazy.grep { (.sigma0 > max) && (max = .sigma0) }.first(20)
}
Output:
[1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560]

Swift[edit]

extension BinaryInteger {
  @inlinable
  public func countDivisors() -> Int {
    var workingN = self
    var count = 1

    while workingN & 1 == 0 {
      workingN >>= 1

      count += 1
    }

    var d = Self(3)

    while d * d <= workingN {
      var (quo, rem) = workingN.quotientAndRemainder(dividingBy: d)

      if rem == 0 {
        var dc = 0

        while rem == 0 {
          dc += count
          workingN = quo

          (quo, rem) = workingN.quotientAndRemainder(dividingBy: d)
        }

        count += dc
      }

      d += 2
    }

    return workingN != 1 ? count * 2 : count
  }
}

var antiPrimes = [Int]()
var maxDivs = 0

for n in 1... {
  guard antiPrimes.count < 20 else {
    break
  }

  let divs = n.countDivisors()

  if maxDivs < divs {
    maxDivs = divs
    antiPrimes.append(n)
  }
}

print("First 20 anti-primes are \(Array(antiPrimes))")
Output:
First 20 anti-primes are [1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560]

Tcl[edit]

Translation of: Java
proc countDivisors {n} {
  if {$n < 2} {return 1}
  set count 2
  set n2 [expr $n / 2]
  for {set i 2} {$i <= $n2} {incr i} {
    if {[expr $n % $i] == 0} {incr count}
  }
  return $count
}

# main
set maxDiv 0
set count 0

puts "The first 20 anti-primes are:"
for {set n 1} {$count < 20} {incr n} {
  set d [countDivisors $n]
  if {$d > $maxDiv} {
    puts $n
    set maxDiv $d
    incr count
  }
}
Output:

./anti_primes.tcl

The first 20 anti-primes are: 1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

Transd[edit]

#lang transd

MainModule: {
    countDivs: (λ n Int() ret_ Int()
        (= ret_ 2)
        (for i in Range(2 (to-Int (/ (to-Double n) 2) 1)) do 
            (if (not (mod n i)) (+= ret_ 1)))
        (ret ret_)
    ),

    _start: (λ locals: max 0 tmp 0 N 1 i 2
        (textout 1 " ")
        (while (< N 20)
            (= tmp (countDivs i))
            (if (> tmp max)
                (textout i " ") (= max tmp) (+= N 1))
            (+= i 1)
    ))
}
Output:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560

Vala[edit]

Translation of: C
int count_divisors(int n) {
  if (n < 2) return 1;
  var count = 2;
  for (int i = 2; i <= n/2; ++i)
    if (n%i == 0) ++count;
  return count;
}
void main() {
  var max_div = 0;
  var count = 0;
  stdout.printf("The first 20 anti-primes are:\n");
  for (int n = 1; count < 20; ++n) {
    var d = count_divisors(n);
    if (d > max_div) {
      stdout.printf("%d ", n);
      max_div = d;
      count++;
    }
  }
  stdout.printf("\n");
}
Output:
The first 20 anti-primes are:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560 

V (Vlang)[edit]

Translation of: go
fn count_divisors(n int) int {
    if n < 2 {
        return 1
    }
    mut count := 2 // 1 and n
    for i := 2; i <= n/2; i++ {
        if n%i == 0 {
            count++
        }
    }
    return count
}
 
fn main() {
    println("The first 20 anti-primes are:")
    mut max_div := 0
    mut count := 0
    for n := 1; count < 20; n++ {
        d := count_divisors(n)
        if d > max_div {
            print("$n ")
            max_div = d
            count++
        }
    }
    println('')
}
Output:
The first 20 anti-primes are:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560 

Wren[edit]

Library: Wren-math
import "/math" for Int

System.print("The first 20 anti-primes are:")
var maxDiv = 0
var count = 0
var n = 1
while (count < 20) {
    var d = Int.divisors(n).count
    if (d > maxDiv) {
       System.write("%(n) ")
       maxDiv = d
       count = count + 1
    }
    n = n + 1
}
System.print()
Output:
The first 20 anti-primes are:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560 

XPL0[edit]

int Counter, Num, Cnt, Div, Max;
[Counter:= 0;
Max:= 0;
Num:= 1;
loop    [Cnt:= 0;
        Div:= 1;
        repeat  if rem(Num/Div) = 0 then Cnt:= Cnt+1;
                Div:= Div+1;
        until   Div > Num;
        if Cnt > Max then
                [IntOut(0, Num);  ChOut(0, ^ );
                Max:= Cnt;
                Counter:= Counter+1;
                if Counter >= 20 then quit;
                ];
        Num:= Num+1;
        ];
]
Output:
1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560 

zkl[edit]

Translation of: Raku
fcn properDivsN(n) //--> count of proper divisors. 1-->1, wrong but OK here
   { [1.. (n + 1)/2 + 1].reduce('wrap(p,i){ p + (n%i==0 and n!=i) }) }
fcn antiPrimes{		// -->iterator
   Walker.chain([2..59],[60..*,30]).tweak(fcn(c,rlast){
      last,mx := rlast.value, properDivsN(c);
      if(mx<=last) return(Void.Skip);
      rlast.set(mx);
      c
   }.fp1(Ref(0))).push(1);	// 1 has no proper divisors
}
println("First 20 anti-primes:\n  ",antiPrimes().walk(20).concat(" "));
Output:
First 20 anti-primes:
  1 2 4 6 12 24 36 48 60 120 180 240 360 720 840 1260 1680 2520 5040 7560