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
  1. Factors of an integer
  2. Sieve of Eratosthenes

 

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

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

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

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

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]

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 

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

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


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]

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 }

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

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
61261200 has 720 dividers
73513440 has 768 dividers
110270160 has 800 dividers
122522400 has 864 dividers
147026880 has 896 dividers
183783600 has 960 dividers
245044800 has 1008 dividers
294053760 has 1024 dividers
367567200 has 1152 dividers
551350800 has 1200 dividers
698377680 has 1280 dividers
735134400 has 1344 dividers
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2095133040 has 1600 dividers
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36802111876251321600 has 207360 dividers
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3941984609400907810540800 has 1658880 dividers
4927480761751134763176000 has 1720320 dividers
5912976914101361715811200 has 1769472 dividers
7883969218801815621081600 has 1843200 dividers
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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
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108404576758524964789872000 has 2949120 dividers
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193814243295544634018256000 has 3145728 dividers

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>

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]

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

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)

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

Perl 6[edit]

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: {[email protected][^(@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

Phix[edit]

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: ") ?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}

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)

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
for c in count(1):
ln = len(factors(c))
if ln > mx:
yield c
mx = ln
 
if __name__ == '__main__':
print(list(islice(antiprimes(), 20)))
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)

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; end /*Even? " " " " 3.*/
/* [↑] 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 /*if no remainder, then found a divisor*/
#=#+2; 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   10%   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. */
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 /*if no remainder, then found a divisor*/
$=$+2; 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]

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 

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 

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

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."

zkl[edit]

Translation of: Perl6
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