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Odd squarefree semiprimes

From Rosetta Code
Odd squarefree semiprimes is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Task

Odd numbers of the form p*q where p and q are distinct primes, where p*q < 1000

ALGOL 68[edit]

BEGIN # find some odd square free semi-primes                    #
# numbers of the form p*q where p =/= q and p, q are prime #
# reurns a list of primes up to n #
PROC prime list = ( INT n )[]INT:
BEGIN
# sieve the primes to n #
INT no = 0, yes = 1;
[ 1 : n ]INT p;
p[ 1 ] := no; p[ 2 ] := yes;
FOR i FROM 3 BY 2 TO n DO p[ i ] := yes OD;
FOR i FROM 4 BY 2 TO n DO p[ i ] := no OD;
FOR i FROM 3 BY 2 TO ENTIER sqrt( n ) DO
IF p[ i ] = yes THEN FOR s FROM i * i BY i + i TO n DO p[ s ] := no OD FI
OD;
# replace the sieve with a list #
INT p pos := 0;
FOR i TO n DO IF p[ i ] = yes THEN p[ p pos +:= 1 ] := i FI OD;
p[ 1 : p pos ]
END # prime list # ;
# show odd square free semi-primes up to 1000 #
INT max number = 1000;
INT max prime = 1 + ( max number OVER 3 ); # the smallest odd prime is 3, so this shuld be enough primes #
[]INT prime = prime list( max prime );
[ 1 : max number ]BOOL numbers; FOR i TO max number DO numbers[ i ] := FALSE OD;
FOR i FROM 2 TO UPB prime - 1 DO
FOR j FROM i + 1 TO UPB prime
WHILE INT pq = prime[ i ] * prime[ j ];
pq < max number
DO
numbers[ pq ] := TRUE
OD
OD;
INT n count := 0;
FOR i TO max number DO
IF numbers[ i ] THEN
print( ( " ", whole( i, -4 ) ) );
n count +:= 1;
IF n count MOD 20 = 0 THEN print( ( newline ) ) FI
FI
OD
END
Output:
   15   21   33   35   39   51   55   57   65   69   77   85   87   91   93   95  111  115  119  123
  129  133  141  143  145  155  159  161  177  183  185  187  201  203  205  209  213  215  217  219
  221  235  237  247  249  253  259  265  267  287  291  295  299  301  303  305  309  319  321  323
  327  329  335  339  341  355  365  371  377  381  391  393  395  403  407  411  413  415  417  427
  437  445  447  451  453  469  471  473  481  485  489  493  497  501  505  511  515  517  519  527
  533  535  537  543  545  551  553  559  565  573  579  581  583  589  591  597  611  623  629  633
  635  649  655  667  669  671  679  681  685  687  689  695  697  699  703  707  713  717  721  723
  731  737  745  749  753  755  763  767  771  779  781  785  789  791  793  799  803  807  813  815
  817  831  835  843  849  851  865  869  871  879  889  893  895  899  901  905  913  917  921  923
  933  939  943  949  951  955  959  965  973  979  985  989  993  995

Arturo[edit]

primes: select 0..1000 => prime?
lst: sort unique flatten map primes 'p [
map select primes 'q -> all? @[odd? p*q p<>q 1000>p*q]=>[p*&]
]
loop split.every:10 lst 'a ->
print map a => [pad to :string & 4]
Output:
  15   21   33   35   39   51   55   57   65   69 
  77   85   87   91   93   95  111  115  119  123 
 129  133  141  143  145  155  159  161  177  183 
 185  187  201  203  205  209  213  215  217  219 
 221  235  237  247  249  253  259  265  267  287 
 291  295  299  301  303  305  309  319  321  323 
 327  329  335  339  341  355  365  371  377  381 
 391  393  395  403  407  411  413  415  417  427 
 437  445  447  451  453  469  471  473  481  485 
 489  493  497  501  505  511  515  517  519  527 
 533  535  537  543  545  551  553  559  565  573 
 579  581  583  589  591  597  611  623  629  633 
 635  649  655  667  669  671  679  681  685  687 
 689  695  697  699  703  707  713  717  721  723 
 731  737  745  749  753  755  763  767  771  779 
 781  785  789  791  793  799  803  807  813  815 
 817  831  835  843  849  851  865  869  871  879 
 889  893  895  899  901  905  913  917  921  923 
 933  939  943  949  951  955  959  965  973  979 
 985  989  993  995

AWK[edit]

 
# syntax: GAWK -f ODD_SQUAREFREE_SEMIPRIMES.AWK
# converted from C++
BEGIN {
start = 1
stop = 999
for (i=start; i<=stop; i+=2) {
if (is_odd_square_free_semiprime(i)) {
printf("%4d%1s",i,++count%10?"":"\n")
}
}
printf("\nOdd Square Free Semiprimes %d-%d: %d\n",start,stop,count)
exit(0)
}
function is_odd_square_free_semiprime(n, count,i) {
if (and(n,1) == 0) {
return(0)
}
for (i=3; i*i<=n; i+=2) {
for (; n%i==0; n=int(n/i)) {
if (++count > 1) {
return(0)
}
}
}
return(count==1)
}
 
Output:
  15   21   33   35   39   51   55   57   65   69
  77   85   87   91   93   95  111  115  119  123
 129  133  141  143  145  155  159  161  177  183
 185  187  201  203  205  209  213  215  217  219
 221  235  237  247  249  253  259  265  267  287
 291  295  299  301  303  305  309  319  321  323
 327  329  335  339  341  355  365  371  377  381
 391  393  395  403  407  411  413  415  417  427
 437  445  447  451  453  469  471  473  481  485
 489  493  497  501  505  511  515  517  519  527
 533  535  537  543  545  551  553  559  565  573
 579  581  583  589  591  597  611  623  629  633
 635  649  655  667  669  671  679  681  685  687
 689  695  697  699  703  707  713  717  721  723
 731  737  745  749  753  755  763  767  771  779
 781  785  789  791  793  799  803  807  813  815
 817  831  835  843  849  851  865  869  871  879
 889  893  895  899  901  905  913  917  921  923
 933  939  943  949  951  955  959  965  973  979
 985  989  993  995
Odd Square Free Semiprimes 1-999: 194

BASIC[edit]

FreeBASIC[edit]

Use the function from Primality by trial division#FreeBASIC as an include. This code generates the odd squarefree semiprimes in ascending order of their first factor, then their second.

#include "isprime.bas"
dim as integer p, q
for p = 3 to 999
if not isprime(p) then continue for
for q = p+1 to 1000\p
if not isprime(q) then continue for
print p*q;" ";
next q
next p
Output:
  15  21  33  39  51  57  69  87  93  111  123  129  141  159  177  183  201  213  219  237  249  267  291  303  309  321  327  339  381  393  411  417  447  453  471  489  501  519  537  543  573  579  591  597  633  669  681  687  699  717  723  753  771  789  807  813  831  843  849  879  921  933  939  951  993  35  55  65  85  95  115  145  155  185  205  215  235  265  295  305  335  355  365  395  415  445  485  505  515  535  545  565  635  655  685  695  745  755  785  815  835  865  895  905  955  965  985  995  77  91  119  133  161  203  217  259  287  301  329  371  413  427  469  497  511  553  581  623  679  707  721  749  763  791  889  917  959  973  143  187  209  253  319  341  407  451  473  517  583  649  671  737  781  803  869  913  979  221  247  299  377  403  481  533  559  611  689  767  793  871  923  949  323  391  493  527  629  697  731  799  901  437  551  589  703  779  817  893  667  713  851  943  989  899

Tiny BASIC[edit]

    LET P = 1
10 LET P = P + 2
LET Q = P
IF P >= 1000 THEN END
LET A = P
GOSUB 100
IF Z = 0 THEN GOTO 10
20 LET Q = Q + 2
IF Q > 1000/P THEN GOTO 10
LET A = Q
GOSUB 100
IF Z = 0 THEN GOTO 20
PRINT P," ",Q," ",P*Q
GOTO 20
100 REM PRIMALITY BY TRIAL DIVISION
LET Z = 1
LET I = 2
110 IF (A/I)*I = A THEN LET Z = 0
IF Z = 0 THEN RETURN
LET I = I + 1
IF I*I <= A THEN GOTO 110
RETURN

C#[edit]

This reveals a set of semi-prime numbers (with exactly two factors for each n), where 1 < p < q < n. It is square-free, since p < q.

using System; using static System.Console; using System.Collections;
using System.Linq; using System.Collections.Generic;
 
class Program { static void Main(string[] args) {
int lmt = 1000, amt, c = 0, sr = (int)Math.Sqrt(lmt), lm2; var res = new List<int>();
var pr = PG.Primes(lmt / 3 + 5).ToArray(); lm2 = pr.OrderBy(i => Math.Abs(sr - i)).First();
lm2 = Array.IndexOf(pr, lm2); for (var p = 0; p < lm2; p++) { amt = 0; for (var q = p + 1; amt < lmt; q++)
res.Add(amt = pr[p] * pr[q]); } res.Sort(); foreach(var item in res.TakeWhile(x => x < lmt))
Write("{0,4} {1}", item, ++c % 20 == 0 ? "\n" : "");
Write("\n\nCounted {0} odd squarefree semiprimes under {1}", c, lmt); } }
 
class PG { public static IEnumerable<int> Primes(int lim) {
var flags = new bool[lim + 1]; int j = 3;
for (int d = 8, sq = 9; sq <= lim; j += 2, sq += d += 8)
if (!flags[j]) { yield return j;
for (int k = sq, i = j << 1; k <= lim; k += i) flags[k] = true; }
for (; j <= lim; j += 2) if (!flags[j]) yield return j; } }
Output:
  15   21   33   35   39   51   55   57   65   69   77   85   87   91   93   95  111  115  119  123 
 129  133  141  143  145  155  159  161  177  183  185  187  201  203  205  209  213  215  217  219 
 221  235  237  247  249  253  259  265  267  287  291  295  299  301  303  305  309  319  321  323 
 327  329  335  339  341  355  365  371  377  381  391  393  395  403  407  411  413  415  417  427 
 437  445  447  451  453  469  471  473  481  485  489  493  497  501  505  511  515  517  519  527 
 533  535  537  543  545  551  553  559  565  573  579  581  583  589  591  597  611  623  629  633 
 635  649  655  667  669  671  679  681  685  687  689  695  697  699  703  707  713  717  721  723 
 731  737  745  749  753  755  763  767  771  779  781  785  789  791  793  799  803  807  813  815 
 817  831  835  843  849  851  865  869  871  879  889  893  895  899  901  905  913  917  921  923 
 933  939  943  949  951  955  959  965  973  979  985  989  993  995 

Counted 194 odd squarefree semiprimes under 1000

C++[edit]

#include <iomanip>
#include <iostream>
 
bool odd_square_free_semiprime(int n) {
if ((n & 1) == 0)
return false;
int count = 0;
for (int i = 3; i * i <= n; i += 2) {
for (; n % i == 0; n /= i) {
if (++count > 1)
return false;
}
}
return count == 1;
}
 
int main() {
const int n = 1000;
std::cout << "Odd square-free semiprimes < " << n << ":\n";
int count = 0;
for (int i = 1; i < n; i += 2) {
if (odd_square_free_semiprime(i)) {
++count;
std::cout << std::setw(4) << i;
if (count % 20 == 0)
std::cout << '\n';
}
}
std::cout << "\nCount: " << count << '\n';
return 0;
}
Output:
Odd square-free semiprimes < 1000:
  15  21  33  35  39  51  55  57  65  69  77  85  87  91  93  95 111 115 119 123
 129 133 141 143 145 155 159 161 177 183 185 187 201 203 205 209 213 215 217 219
 221 235 237 247 249 253 259 265 267 287 291 295 299 301 303 305 309 319 321 323
 327 329 335 339 341 355 365 371 377 381 391 393 395 403 407 411 413 415 417 427
 437 445 447 451 453 469 471 473 481 485 489 493 497 501 505 511 515 517 519 527
 533 535 537 543 545 551 553 559 565 573 579 581 583 589 591 597 611 623 629 633
 635 649 655 667 669 671 679 681 685 687 689 695 697 699 703 707 713 717 721 723
 731 737 745 749 753 755 763 767 771 779 781 785 789 791 793 799 803 807 813 815
 817 831 835 843 849 851 865 869 871 879 889 893 895 899 901 905 913 917 921 923
 933 939 943 949 951 955 959 965 973 979 985 989 993 995
Count: 194

Factor[edit]

Works with: Factor version 0.99 2021-02-05
USING: combinators.short-circuit formatting grouping io kernel
math.primes.factors math.ranges prettyprint sequences sets ;
 
: sq-free-semiprime? ( n -- ? )
factors { [ length 2 = ] [ all-unique? ] } 1&& ;
 
: odd-sfs-upto ( n -- seq )
1 swap 2 <range> [ sq-free-semiprime? ] filter ;
 
999 odd-sfs-upto dup length
"Found %d odd square-free semiprimes < 1000:\n" printf
20 group [ [ "%4d" printf ] each nl ] each nl
Output:
Found 194 odd square-free semiprimes < 1000:
  15  21  33  35  39  51  55  57  65  69  77  85  87  91  93  95 111 115 119 123
 129 133 141 143 145 155 159 161 177 183 185 187 201 203 205 209 213 215 217 219
 221 235 237 247 249 253 259 265 267 287 291 295 299 301 303 305 309 319 321 323
 327 329 335 339 341 355 365 371 377 381 391 393 395 403 407 411 413 415 417 427
 437 445 447 451 453 469 471 473 481 485 489 493 497 501 505 511 515 517 519 527
 533 535 537 543 545 551 553 559 565 573 579 581 583 589 591 597 611 623 629 633
 635 649 655 667 669 671 679 681 685 687 689 695 697 699 703 707 713 717 721 723
 731 737 745 749 753 755 763 767 771 779 781 785 789 791 793 799 803 807 813 815
 817 831 835 843 849 851 865 869 871 879 889 893 895 899 901 905 913 917 921 923
 933 939 943 949 951 955 959 965 973 979 985 989 993 995

Forth[edit]

Works with: Gforth
: odd-square-free-semi-prime? { n -- ? }
n 1 and 0= if false exit then
0 { count }
3
begin
dup dup * n <=
while
begin
dup n swap mod 0=
while
count 1+ to count
count 1 > if
drop false exit
then
dup n swap / to n
repeat
2 +
repeat
drop
count 1 = ;
 
: special_odd_numbers ( n -- )
." Odd square-free semiprimes < " dup 1 .r ." :" cr
0 swap
1 do
i odd-square-free-semi-prime? if
1+
i 4 .r
dup 20 mod 0= if cr then
then
2 +loop
cr ." Count: " . cr ;
 
1000 special_odd_numbers
bye
Output:
Odd square-free semiprimes < 1000:
  15  21  33  35  39  51  55  57  65  69  77  85  87  91  93  95 111 115 119 123
 129 133 141 143 145 155 159 161 177 183 185 187 201 203 205 209 213 215 217 219
 221 235 237 247 249 253 259 265 267 287 291 295 299 301 303 305 309 319 321 323
 327 329 335 339 341 355 365 371 377 381 391 393 395 403 407 411 413 415 417 427
 437 445 447 451 453 469 471 473 481 485 489 493 497 501 505 511 515 517 519 527
 533 535 537 543 545 551 553 559 565 573 579 581 583 589 591 597 611 623 629 633
 635 649 655 667 669 671 679 681 685 687 689 695 697 699 703 707 713 717 721 723
 731 737 745 749 753 755 763 767 771 779 781 785 789 791 793 799 803 807 813 815
 817 831 835 843 849 851 865 869 871 879 889 893 895 899 901 905 913 917 921 923
 933 939 943 949 951 955 959 965 973 979 985 989 993 995
Count: 194 

Go[edit]

Translation of: Wren
Library: Go-rcu
package main
 
import (
"fmt"
"rcu"
"sort"
)
 
func main() {
primes := rcu.Primes(333)
var oss []int
for i := 1; i < len(primes)-1; i++ {
for j := i + 1; j < len(primes); j++ {
n := primes[i] * primes[j]
if n >= 1000 {
break
}
oss = append(oss, n)
}
}
sort.Ints(oss)
fmt.Println("Odd squarefree semiprimes under 1,000:")
for i, n := range oss {
fmt.Printf("%3d ", n)
if (i+1)%10 == 0 {
fmt.Println()
}
}
fmt.Printf("\n\n%d such numbers found.\n", len(oss))
}
Output:
Odd squarefree semiprimes under 1,000:
 15  21  33  35  39  51  55  57  65  69 
 77  85  87  91  93  95 111 115 119 123 
129 133 141 143 145 155 159 161 177 183 
185 187 201 203 205 209 213 215 217 219 
221 235 237 247 249 253 259 265 267 287 
291 295 299 301 303 305 309 319 321 323 
327 329 335 339 341 355 365 371 377 381 
391 393 395 403 407 411 413 415 417 427 
437 445 447 451 453 469 471 473 481 485 
489 493 497 501 505 511 515 517 519 527 
533 535 537 543 545 551 553 559 565 573 
579 581 583 589 591 597 611 623 629 633 
635 649 655 667 669 671 679 681 685 687 
689 695 697 699 703 707 713 717 721 723 
731 737 745 749 753 755 763 767 771 779 
781 785 789 791 793 799 803 807 813 815 
817 831 835 843 849 851 865 869 871 879 
889 893 895 899 901 905 913 917 921 923 
933 939 943 949 951 955 959 965 973 979 
985 989 993 995 

194 such numbers found.

Julia[edit]

using Primes
 
twoprimeproduct(n) = (a = factor(n).pe; length(a) == 2 && all(p -> p[2] == 1, a))
 
special1k = filter(n -> isodd(n) && twoprimeproduct(n), 1:1000)
 
foreach(p -> print(rpad(p[2], 4), p[1] % 20 == 0 ? "\n" : ""), enumerate(special1k))
 
Output:
15  21  33  35  39  51  55  57  65  69  77  85  87  91  93  95  111 115 119 123 
129 133 141 143 145 155 159 161 177 183 185 187 201 203 205 209 213 215 217 219
221 235 237 247 249 253 259 265 267 287 291 295 299 301 303 305 309 319 321 323
327 329 335 339 341 355 365 371 377 381 391 393 395 403 407 411 413 415 417 427
437 445 447 451 453 469 471 473 481 485 489 493 497 501 505 511 515 517 519 527
533 535 537 543 545 551 553 559 565 573 579 581 583 589 591 597 611 623 629 633
635 649 655 667 669 671 679 681 685 687 689 695 697 699 703 707 713 717 721 723
731 737 745 749 753 755 763 767 771 779 781 785 789 791 793 799 803 807 813 815
817 831 835 843 849 851 865 869 871 879 889 893 895 899 901 905 913 917 921 923
933 939 943 949 951 955 959 965 973 979 985 989 993 995

Nim[edit]

import algorithm, strutils, sugar
 
const
M = 1000 - 1
N = M div 3 # Minimal value for "p" is 3.
 
# Sieve of Eratosthenes.
var composite: array[3..N, bool]
 
for n in countup(3, N, 2):
let n2 = n * n
if n2 > N: break
if not composite[n]:
for k in countup(n2, N, 2 * n):
composite[k] = true
 
let primes = collect(newSeq):
for n in countup(3, N, 2):
if not composite[n]: n
 
var result: seq[int]
for i in 0..<primes.high:
let p = primes[i]
for j in (i+1)..primes.high:
let q = primes[j]
if p * q > M: break
result.add p * q
result.sort()
 
for i, n in result:
stdout.write ($n).align(3), if (i + 1) mod 20 == 0: '\n' else: ' '
echo()
Output:
 15  21  33  35  39  51  55  57  65  69  77  85  87  91  93  95 111 115 119 123
129 133 141 143 145 155 159 161 177 183 185 187 201 203 205 209 213 215 217 219
221 235 237 247 249 253 259 265 267 287 291 295 299 301 303 305 309 319 321 323
327 329 335 339 341 355 365 371 377 381 391 393 395 403 407 411 413 415 417 427
437 445 447 451 453 469 471 473 481 485 489 493 497 501 505 511 515 517 519 527
533 535 537 543 545 551 553 559 565 573 579 581 583 589 591 597 611 623 629 633
635 649 655 667 669 671 679 681 685 687 689 695 697 699 703 707 713 717 721 723
731 737 745 749 753 755 763 767 771 779 781 785 789 791 793 799 803 807 813 815
817 831 835 843 849 851 865 869 871 879 889 893 895 899 901 905 913 917 921 923
933 939 943 949 951 955 959 965 973 979 985 989 993 995 

PARI/GP[edit]

for(s=3, 999, f=factor(s); m=matsize(f); if(s%2==1&&m[1]==2&&f[1,2]==1&&f[2,2]==1, print(s)))

Perl[edit]

#!/usr/bin/perl
 
use strict; # https://rosettacode.org/wiki/Odd_squarefree_semiprimes
use warnings;
 
my (@primes, @found) = grep $_ & 1 && (1 x $_) !~ /^(11+)\1+$/, 3 .. 999 / 3;
"@primes" =~ /\b(\d+)\b.*?\b(\d+)\b(?{ $found[$1 * $2] = $1 * $2 })(*FAIL)/;
print "@{[ grep $_, @found[3 .. 999] ]}\n" =~ s/.{75}\K /\n/gr;
Output:
15 21 33 35 39 51 55 57 65 69 77 85 87 91 93 95 111 115 119 123 129 133 141
143 145 155 159 161 177 183 185 187 201 203 205 209 213 215 217 219 221 235
237 247 249 253 259 265 267 287 291 295 299 301 303 305 309 319 321 323 327
329 335 339 341 355 365 371 377 381 391 393 395 403 407 411 413 415 417 427
437 445 447 451 453 469 471 473 481 485 489 493 497 501 505 511 515 517 519
527 533 535 537 543 545 551 553 559 565 573 579 581 583 589 591 597 611 623
629 633 635 649 655 667 669 671 679 681 685 687 689 695 697 699 703 707 713
717 721 723 731 737 745 749 753 755 763 767 771 779 781 785 789 791 793 799
803 807 813 815 817 831 835 843 849 851 865 869 871 879 889 893 895 899 901
905 913 917 921 923 933 939 943 949 951 955 959 965 973 979 985 989 993 995

Phix[edit]

function oss(integer n)
    sequence f = prime_factors(n,true)
    return length(f)==2 and f[1]!=f[2]
end function
sequence res = apply(true,sprintf,{{"%d"},filter(tagset(999,1,2),oss)})
printf(1,"Found %d odd square-free semiprimes less than 1,000:\n %s\n",
         {length(res),join(shorten(res,"",5),", ")})
Output:
Found 194 odd square-free semiprimes less than 1,000:
 15, 21, 33, 35, 39, ..., 979, 985, 989, 993, 995

Raku[edit]

say (3..333).grep(*.is-prime).combinations(2)».map( * * * ).flat\
.grep( * < 1000 ).sort.batch(20)».fmt('%3d').join: "\n";
Output:
 15  21  33  35  39  51  55  57  65  69  77  85  87  91  93  95 111 115 119 123
129 133 141 143 145 155 159 161 177 183 185 187 201 203 205 209 213 215 217 219
221 235 237 247 249 253 259 265 267 287 291 295 299 301 303 305 309 319 321 323
327 329 335 339 341 355 365 371 377 381 391 393 395 403 407 411 413 415 417 427
437 445 447 451 453 469 471 473 481 485 489 493 497 501 505 511 515 517 519 527
533 535 537 543 545 551 553 559 565 573 579 581 583 589 591 597 611 623 629 633
635 649 655 667 669 671 679 681 685 687 689 695 697 699 703 707 713 717 721 723
731 737 745 749 753 755 763 767 771 779 781 785 789 791 793 799 803 807 813 815
817 831 835 843 849 851 865 869 871 879 889 893 895 899 901 905 913 917 921 923
933 939 943 949 951 955 959 965 973 979 985 989 993 995

REXX[edit]

/*REXX pgm finds odd squarefree semiprimes (product of 2 primes)  that are less then N. */
parse arg hi cols . /*obtain optional argument from the CL.*/
if hi=='' | hi=="," then hi= 1000 /* " " " " " " */
if cols=='' | cols=="," then cols= 10 /* " " " " " " */
call genP /*build array of semaphores for primes.*/
w= 10 /*width of a number in any column. */
@oss= ' odd squarefree semiprimes < ' commas(1000)
if cols>0 then say ' index │'center(@oss, 1 + cols*(w+1) )
if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─')
idx= 1 /*initialize the index of output lines.*/
$=; ss.= 0 /*a list of odd squarefree semiprimes. */
do j=2 while @.j < hi /*gen odd squarefree semiprimes < HI.*/
do k=j+1 while @.k < hi; _= @.j*@.k /*ensure primes are squarefree & < HI.*/
if _>=hi then leave /*Is the product ≥ HI? Then skip it. */
ss._= 1 /*mark # as being squarefree semiprime.*/
end /*k*/
end /*j*/
oss= 0 /*number of odd squarefree semiprimes. */
do m=3 by 2 to hi-1 /*search a list of possible candicates.*/
if \ss.m then iterate /*Does this number exist? No, skip it.*/
oss= oss + 1 /*bump count of odd sq─free semiprimes.*/
if cols==0 then iterate /*Build the list (to be shown later)? */
$= $ right( commas(m), w) /*add an odd square─free semiprime. */
if oss//cols\==0 then iterate /*have we populated a line of output? */
say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */
idx= idx + cols /*bump the index count for the output*/
end /*m*/
 
if $\=='' then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/
if cols>0 then say '───────┴'center("" , 1 + cols*(w+1), '─')
say
say 'Found ' commas(oss) @oss
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?
/*──────────────────────────────────────────────────────────────────────────────────────*/
genP: @.1=2; @.2=3; @.3=5; @.4=7; @.5=11; #= 5 /*define low primes; # of primes so far*/
s.#= @.# **2 /*the highest prime squared (so far). */
/* [↓] generate more primes ≤ high.*/
do [email protected].#+2 by 2 to hi+1 /*find odd primes from here on. */
parse var j '' -1 _; if _==5 then iterate /*J divisible by 5? (right dig)*/
if j// 3==0 then iterate /*" " " 3? */
if j// 7==0 then iterate /*" " " 7? */
do k=5 while s.k<=j /* [↓] divide by the known odd primes.*/
if j//@.k==0 then iterate j /*Is J ÷ X? Then not prime. ___ */
end /*k*/ /* [↑] only process numbers ≤ √ J */
#= #+1; @.#= j; s.#= j*j /*bump # Ps; assign next P; P squared*/
end /*j*/; return
output   when using the default inputs:
 index │                                      odd squarefree semiprimes  <   1,000
───────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────
   1   │         15         21         33         35         39         51         55         57         65         69
  11   │         77         85         87         91         93         95        111        115        119        123
  21   │        129        133        141        143        145        155        159        161        177        183
  31   │        185        187        201        203        205        209        213        215        217        219
  41   │        221        235        237        247        249        253        259        265        267        287
  51   │        291        295        299        301        303        305        309        319        321        323
  61   │        327        329        335        339        341        355        365        371        377        381
  71   │        391        393        395        403        407        411        413        415        417        427
  81   │        437        445        447        451        453        469        471        473        481        485
  91   │        489        493        497        501        505        511        515        517        519        527
  101  │        533        535        537        543        545        551        553        559        565        573
  111  │        579        581        583        589        591        597        611        623        629        633
  121  │        635        649        655        667        669        671        679        681        685        687
  131  │        689        695        697        699        703        707        713        717        721        723
  141  │        731        737        745        749        753        755        763        767        771        779
  151  │        781        785        789        791        793        799        803        807        813        815
  161  │        817        831        835        843        849        851        865        869        871        879
  171  │        889        893        895        899        901        905        913        917        921        923
  181  │        933        939        943        949        951        955        959        965        973        979
  191  │        985        989        993        995
───────┴───────────────────────────────────────────────────────────────────────────────────────────────────────────────

Found  194  odd squarefree semiprimes  <   1,000

Ring[edit]

load "stdlib.ring" # for isprime() function
? "working..." + nl + "Odd squarefree semiprimes are:"
 
limit = 1000 Prim = []
 
# create table of prime numbers from 3 to 1000 / 3
pr = []
for n = 3 to 1000 / 3
if isprime(n) Add(pr,n) ok
next pl = len(pr)
 
# calculate upper limit for n
for nlim = 1 to pl
if pr[nlim] * pr[nlim] > limit exit ok
next nlim--
 
# add items to result list and sort
for n = 1 to nlim
for m = n + 1 to pl
amt = pr[n] * pr[m]
if amt > limit exit ok
add(Prim, amt)
next
next Prim = sort(Prim)
 
# display results
for n = 1 to len(Prim)
see sf(Prim[n], 4) + " "
if n % 20 = 0 see nl ok
next n--
 
? nl + nl + "Found " + n + " Odd squarefree semiprimes." + nl + "done..."
 
# a very plain string formatter, intended to even up columnar outputs
def sf x, y
s = string(x) l = len(s)
if l > y y = l ok
return substr(" ", 11 - y + l) + s
Output:
working...
Odd squarefree semiprimes are:
  15   21   33   35   39   51   55   57   65   69   77   85   87   91   93   95  111  115  119  123 
 129  133  141  143  145  155  159  161  177  183  185  187  201  203  205  209  213  215  217  219 
 221  235  237  247  249  253  259  265  267  287  291  295  299  301  303  305  309  319  321  323 
 327  329  335  339  341  355  365  371  377  381  391  393  395  403  407  411  413  415  417  427 
 437  445  447  451  453  469  471  473  481  485  489  493  497  501  505  511  515  517  519  527 
 533  535  537  543  545  551  553  559  565  573  579  581  583  589  591  597  611  623  629  633 
 635  649  655  667  669  671  679  681  685  687  689  695  697  699  703  707  713  717  721  723 
 731  737  745  749  753  755  763  767  771  779  781  785  789  791  793  799  803  807  813  815 
 817  831  835  843  849  851  865  869  871  879  889  893  895  899  901  905  913  917  921  923 
 933  939  943  949  951  955  959  965  973  979  985  989  993  995 

Found 194 Odd squarefree semiprimes.
done...

Wren[edit]

Library: Wren-math
Library: Wren-seq
Library: Wren-fmt
Library: Wren-sort
import "/math" for Int
import "/seq" for Lst
import "/fmt" for Fmt
import "/sort" for Sort
 
var primes = Int.primeSieve(333)
var oss = []
for (i in 1...primes.count-1) {
for (j in i + 1...primes.count) {
var n = primes[i] * primes[j]
if (n >= 1000) break
oss.add(n)
}
}
Sort.quick(oss)
System.print("Odd squarefree semiprimes under 1,000:")
for (chunk in Lst.chunks(oss, 10)) Fmt.print("$3d", chunk)
System.print("\n%(oss.count) such numbers found.")
Output:
Odd squarefree semiprimes under 1,000:
 15  21  33  35  39  51  55  57  65  69
 77  85  87  91  93  95 111 115 119 123
129 133 141 143 145 155 159 161 177 183
185 187 201 203 205 209 213 215 217 219
221 235 237 247 249 253 259 265 267 287
291 295 299 301 303 305 309 319 321 323
327 329 335 339 341 355 365 371 377 381
391 393 395 403 407 411 413 415 417 427
437 445 447 451 453 469 471 473 481 485
489 493 497 501 505 511 515 517 519 527
533 535 537 543 545 551 553 559 565 573
579 581 583 589 591 597 611 623 629 633
635 649 655 667 669 671 679 681 685 687
689 695 697 699 703 707 713 717 721 723
731 737 745 749 753 755 763 767 771 779
781 785 789 791 793 799 803 807 813 815
817 831 835 843 849 851 865 869 871 879
889 893 895 899 901 905 913 917 921 923
933 939 943 949 951 955 959 965 973 979
985 989 993 995

194 such numbers found.