N-smooth numbers

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

n-smooth   numbers are positive integers which have no prime factors > n.

The   n   (when using it in the expression)   n-smooth   is always prime,
there are   no   9-smooth numbers.

1   (unity)   is always included in n-smooth numbers.



2-smooth   numbers are non-negative powers of two.
5-smooth   numbers are also called   Hamming numbers.
7-smooth   numbers are also called    humble   numbers.


A way to express   11-smooth   numbers is:

  11-smooth  =  2i × 3j × 5k × 7m × 11p
           where     i, j, k, m, p ≥ 0


Task
  •   show the first   25   n-smooth numbers   for   n=2   ───►   n=29
  •   show   three numbers starting with   3,000   n-smooth numbers   for   n=3   ───►   n=29
  •   show twenty numbers starting with  30,000   n-smooth numbers   for   n=503   ───►   n=521   (optional)


All ranges   (for   n)   are to be inclusive, and only prime numbers are to be used.
The (optional) n-smooth numbers for the third range are:   503,   509,   and   521.
Show all n-smooth numbers for any particular   n   in a horizontal list.
Show all output here on this page.


Related tasks


References




C#[edit]

Translation of: D
using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
 
namespace NSmooth {
class Program {
static readonly List<BigInteger> primes = new List<BigInteger>();
static readonly List<int> smallPrimes = new List<int>();
 
static Program() {
primes.Add(2);
smallPrimes.Add(2);
 
BigInteger i = 3;
while (i <= 521) {
if (IsPrime(i)) {
primes.Add(i);
if (i <= 29) {
smallPrimes.Add((int)i);
}
}
i += 2;
}
}
 
static bool IsPrime(BigInteger value) {
if (value < 2) return false;
 
if (value % 2 == 0) return value == 2;
if (value % 3 == 0) return value == 3;
 
if (value % 5 == 0) return value == 5;
if (value % 7 == 0) return value == 7;
 
if (value % 11 == 0) return value == 11;
if (value % 13 == 0) return value == 13;
 
if (value % 17 == 0) return value == 17;
if (value % 19 == 0) return value == 19;
 
if (value % 23 == 0) return value == 23;
 
BigInteger t = 29;
while (t * t < value) {
if (value % t == 0) return false;
value += 2;
 
if (value % t == 0) return false;
value += 4;
}
 
return true;
}
 
static List<BigInteger> NSmooth(int n, int size) {
if (n < 2 || n > 521) {
throw new ArgumentOutOfRangeException("n");
}
if (size < 1) {
throw new ArgumentOutOfRangeException("size");
}
 
BigInteger bn = n;
bool ok = false;
foreach (var prime in primes) {
if (bn == prime) {
ok = true;
break;
}
}
if (!ok) {
throw new ArgumentException("must be a prime number", "n");
}
 
BigInteger[] ns = new BigInteger[size];
ns[0] = 1;
for (int i = 1; i < size; i++) {
ns[i] = 0;
}
 
List<BigInteger> next = new List<BigInteger>();
foreach (var prime in primes) {
if (prime > bn) {
break;
}
next.Add(prime);
}
 
int[] indices = new int[next.Count];
for (int i = 0; i < indices.Length; i++) {
indices[i] = 0;
}
for (int m = 1; m < size; m++) {
ns[m] = next.Min();
for (int i = 0; i < indices.Length; i++) {
if (ns[m] == next[i]) {
indices[i]++;
next[i] = primes[i] * ns[indices[i]];
}
}
}
 
return ns.ToList();
}
 
static void Println<T>(IEnumerable<T> nums) {
Console.Write('[');
 
var it = nums.GetEnumerator();
if (it.MoveNext()) {
Console.Write(it.Current);
}
while (it.MoveNext()) {
Console.Write(", ");
Console.Write(it.Current);
}
 
Console.WriteLine(']');
}
 
static void Main() {
foreach (var i in smallPrimes) {
Console.WriteLine("The first {0}-smooth numbers are:", i);
Println(NSmooth(i, 25));
Console.WriteLine();
}
foreach (var i in smallPrimes.Skip(1)) {
Console.WriteLine("The 3,000 to 3,202 {0}-smooth numbers are:", i);
Println(NSmooth(i, 3_002).Skip(2_999));
Console.WriteLine();
}
foreach (var i in new int[] { 503, 509, 521 }) {
Console.WriteLine("The 30,000 to 3,019 {0}-smooth numbers are:", i);
Println(NSmooth(i, 30_019).Skip(29_999));
Console.WriteLine();
}
}
}
}
Output:
The first 2-smooth numbers are:
[1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216]

The first 3-smooth numbers are:
[1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 128, 144, 162, 192]

The first 5-smooth numbers are:
[1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54]

The first 7-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36]

The first 11-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32]

The first 13-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28]

The first 17-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 27]

The first 19-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26]

The first 23-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]

The first 29-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]

The 3,000 to 3,202 3-smooth numbers are:
[91580367978306252441724649472, 92829823186414819915547541504, 94096325042746502515294076928]

The 3,000 to 3,202 5-smooth numbers are:
[278942752080, 279936000000, 281250000000]

The 3,000 to 3,202 7-smooth numbers are:
[50176000, 50331648, 50388480]

The 3,000 to 3,202 11-smooth numbers are:
[2112880, 2116800, 2117016]

The 3,000 to 3,202 13-smooth numbers are:
[390000, 390390, 390625]

The 3,000 to 3,202 17-smooth numbers are:
[145800, 145860, 146016]

The 3,000 to 3,202 19-smooth numbers are:
[74256, 74358, 74360]

The 3,000 to 3,202 23-smooth numbers are:
[46552, 46575, 46585]

The 3,000 to 3,202 29-smooth numbers are:
[33516, 33524, 33534]

The 30,000 to 3,019 503-smooth numbers are:
[62913, 62914, 62916, 62918, 62920, 62923, 62926, 62928, 62930, 62933, 62935, 62937, 62944, 62946, 62951, 62952, 62953, 62957, 62959, 62964]

The 30,000 to 3,019 509-smooth numbers are:
[62601, 62602, 62604, 62607, 62608, 62609, 62611, 62618, 62620, 62622, 62624, 62625, 62626, 62628, 62629, 62634, 62640, 62643, 62645, 62646]

The 30,000 to 3,019 521-smooth numbers are:
[62287, 62288, 62291, 62292, 62300, 62304, 62307, 62308, 62310, 62315, 62320, 62321, 62322, 62325, 62328, 62329, 62330, 62331, 62335, 62336]

D[edit]

Translation of: Kotlin
import std.algorithm;
import std.bigint;
import std.exception;
import std.range;
import std.stdio;
 
BigInt[] primes;
int[] smallPrimes;
 
bool isPrime(BigInt value) {
if (value < 2) return false;
 
if (value % 2 == 0) return value == 2;
if (value % 3 == 0) return value == 3;
 
if (value % 5 == 0) return value == 5;
if (value % 7 == 0) return value == 7;
 
if (value % 11 == 0) return value == 11;
if (value % 13 == 0) return value == 13;
 
if (value % 17 == 0) return value == 17;
if (value % 19 == 0) return value == 19;
 
if (value % 23 == 0) return value == 23;
 
BigInt t = 29;
while (t * t < value) {
if (value % t == 0) return false;
value += 2;
 
if (value % t == 0) return false;
value += 4;
}
 
return true;
}
 
// cache all primes up to 521
void init() {
primes ~= BigInt(2);
smallPrimes ~= 2;
 
BigInt i = 3;
while (i <= 521) {
if (isPrime(i)) {
primes ~= i;
if (i <= 29) {
smallPrimes ~= i.toInt;
}
}
i += 2;
}
}
 
BigInt[] nSmooth(int n, int size)
in {
enforce(n >= 2 && n <= 521, "n must be between 2 and 521");
enforce(size > 1, "size must be at least 1");
}
do {
BigInt bn = n;
bool ok = false;
foreach (prime; primes) {
if (bn == prime) {
ok = true;
break;
}
}
enforce(ok, "n must be a prime number");
 
BigInt[] ns;
ns.length = size;
ns[] = BigInt(0);
ns[0] = 1;
 
BigInt[] next;
foreach(prime; primes) {
if (prime > bn) {
break;
}
next ~= prime;
}
 
int[] indicies;
indicies.length = next.length;
indicies[] = 0;
foreach (m; 1 .. size) {
ns[m] = next.reduce!min;
foreach (i,v; indicies) {
if (ns[m] == next[i]) {
indicies[i]++;
next[i] = primes[i] * ns[indicies[i]];
}
}
}
 
return ns;
}
 
void main() {
init();
 
foreach (i; smallPrimes) {
writeln("The first ", i, "-smooth numbers are:");
writeln(nSmooth(i, 25));
writeln;
}
foreach (i; smallPrimes.drop(1)) {
writeln("The 3,000th to 3,202 ", i, "-smooth numbers are:");
writeln(nSmooth(i, 3_002).drop(2_999));
writeln;
}
foreach (i; [503, 509, 521]) {
writeln("The 30,000th to 30,019 ", i, "-smooth numbers are:");
writeln(nSmooth(i, 30_019).drop(29_999));
writeln;
}
}
Output:
The first 2-smooth numbers are:
[1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216]

The first 3-smooth numbers are:
[1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 128, 144, 162, 192]

The first 5-smooth numbers are:
[1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54]

The first 7-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36]

The first 11-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32]

The first 13-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28]

The first 17-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 27]

The first 19-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26]

The first 23-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]

The first 29-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]

The 3,000th to 3,202 3-smooth numbers are:
[91580367978306252441724649472, 92829823186414819915547541504, 94096325042746502515294076928]

The 3,000th to 3,202 5-smooth numbers are:
[278942752080, 279936000000, 281250000000]

The 3,000th to 3,202 7-smooth numbers are:
[50176000, 50331648, 50388480]

The 3,000th to 3,202 11-smooth numbers are:
[2112880, 2116800, 2117016]

The 3,000th to 3,202 13-smooth numbers are:
[390000, 390390, 390625]

The 3,000th to 3,202 17-smooth numbers are:
[145800, 145860, 146016]

The 3,000th to 3,202 19-smooth numbers are:
[74256, 74358, 74360]

The 3,000th to 3,202 23-smooth numbers are:
[46552, 46575, 46585]

The 3,000th to 3,202 29-smooth numbers are:
[33516, 33524, 33534]

The 30,000th to 30,019 503-smooth numbers are:
[62913, 62914, 62916, 62918, 62920, 62923, 62926, 62928, 62930, 62933, 62935, 62937, 62944, 62946, 62951, 62952, 62953, 62957, 62959, 62964]

The 30,000th to 30,019 509-smooth numbers are:
[62601, 62602, 62604, 62607, 62608, 62609, 62611, 62618, 62620, 62622, 62624, 62625, 62626, 62628, 62629, 62634, 62640, 62643, 62645, 62646]

The 30,000th to 30,019 521-smooth numbers are:
[62287, 62288, 62291, 62292, 62300, 62304, 62307, 62308, 62310, 62315, 62320, 62321, 62322, 62325, 62328, 62329, 62330, 62331, 62335, 62336]

Factor[edit]

USING: deques dlists formatting fry io kernel locals make math
math.order math.primes math.text.english namespaces prettyprint
sequences tools.memory.private ;
IN: rosetta-code.n-smooth-numbers
 
SYMBOL: primes
 
: ns ( n -- seq )
primes-upto [ primes set ] [ length [ 1 1dlist ] replicate ]
bi ;
 
: enqueue ( n seq -- )
[ primes get ] 2dip [ '[ _ * ] map ] dip [ push-back ] 2each
 ;
 
: next ( seq -- n )
dup [ peek-front ] map infimum
[ '[ dup peek-front _ = [ pop-front* ] [ drop ] if ] each ]
[ swap enqueue ] [ nip ] 2tri ;
 
: next-n ( seq n -- seq )
swap '[ _ [ _ next , ] times ] { } make ;
 
:: n-smooth ( n from to -- seq )
n ns to next-n to from - 1 + tail* ;
 
:: show-smooth ( plo phi lo hi -- )
plo phi primes-between [
 :> p lo commas lo ordinal-suffix hi commas hi
ordinal-suffix p "%s%s through %s%s %d-smooth numbers: "
printf p lo hi n-smooth [ pprint bl ] each nl
] each ;
 
: smooth-numbers-demo ( -- )
2 29 1 25 show-smooth nl
3 29 3000 3002 show-smooth nl
503 521 30,000 30,019 show-smooth ;
 
MAIN: smooth-numbers-demo
Output:
1st through 25th 2-smooth numbers: 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 2097152 4194304 8388608 16777216 
1st through 25th 3-smooth numbers: 1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 81 96 108 128 144 162 192 
1st through 25th 5-smooth numbers: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 32 36 40 45 48 50 54 
1st through 25th 7-smooth numbers: 1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36 
1st through 25th 11-smooth numbers: 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 18 20 21 22 24 25 27 28 30 32 
1st through 25th 13-smooth numbers: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 21 22 24 25 26 27 28 
1st through 25th 17-smooth numbers: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 24 25 26 27 
1st through 25th 19-smooth numbers: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 25 26 
1st through 25th 23-smooth numbers: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 
1st through 25th 29-smooth numbers: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 

3,000th through 3,002nd 3-smooth numbers: 91580367978306252441724649472 92829823186414819915547541504 94096325042746502515294076928 
3,000th through 3,002nd 5-smooth numbers: 278942752080 279936000000 281250000000 
3,000th through 3,002nd 7-smooth numbers: 50176000 50331648 50388480 
3,000th through 3,002nd 11-smooth numbers: 2112880 2116800 2117016 
3,000th through 3,002nd 13-smooth numbers: 390000 390390 390625 
3,000th through 3,002nd 17-smooth numbers: 145800 145860 146016 
3,000th through 3,002nd 19-smooth numbers: 74256 74358 74360 
3,000th through 3,002nd 23-smooth numbers: 46552 46575 46585 
3,000th through 3,002nd 29-smooth numbers: 33516 33524 33534 

30,000th through 30,019th 503-smooth numbers: 62913 62914 62916 62918 62920 62923 62926 62928 62930 62933 62935 62937 62944 62946 62951 62952 62953 62957 62959 62964 
30,000th through 30,019th 509-smooth numbers: 62601 62602 62604 62607 62608 62609 62611 62618 62620 62622 62624 62625 62626 62628 62629 62634 62640 62643 62645 62646 
30,000th through 30,019th 521-smooth numbers: 62287 62288 62291 62292 62300 62304 62307 62308 62310 62315 62320 62321 62322 62325 62328 62329 62330 62331 62335 62336 

Go[edit]

package main
 
import (
"fmt"
"log"
"math/big"
)
 
var (
primes []*big.Int
smallPrimes []int
)
 
// cache all primes up to 521
func init() {
two := big.NewInt(2)
three := big.NewInt(3)
p521 := big.NewInt(521)
p29 := big.NewInt(29)
primes = append(primes, two)
smallPrimes = append(smallPrimes, 2)
for i := three; i.Cmp(p521) <= 0; i.Add(i, two) {
if i.ProbablyPrime(0) {
primes = append(primes, new(big.Int).Set(i))
if i.Cmp(p29) <= 0 {
smallPrimes = append(smallPrimes, int(i.Int64()))
}
}
}
}
 
func min(bs []*big.Int) *big.Int {
if len(bs) == 0 {
log.Fatal("slice must have at least one element")
}
res := bs[0]
for _, i := range bs[1:] {
if i.Cmp(res) < 0 {
res = i
}
}
return res
}
 
func nSmooth(n, size int) []*big.Int {
if n < 2 || n > 521 {
log.Fatal("n must be between 2 and 521")
}
if size < 1 {
log.Fatal("size must be at least 1")
}
bn := big.NewInt(int64(n))
ok := false
for _, prime := range primes {
if bn.Cmp(prime) == 0 {
ok = true
break
}
}
if !ok {
log.Fatal("n must be a prime number")
}
 
ns := make([]*big.Int, size)
ns[0] = big.NewInt(1)
var next []*big.Int
for i := 0; i < len(primes); i++ {
if primes[i].Cmp(bn) > 0 {
break
}
next = append(next, new(big.Int).Set(primes[i]))
}
indices := make([]int, len(next))
for m := 1; m < size; m++ {
ns[m] = new(big.Int).Set(min(next))
for i := 0; i < len(indices); i++ {
if ns[m].Cmp(next[i]) == 0 {
indices[i]++
next[i].Mul(primes[i], ns[indices[i]])
}
}
}
return ns
}
 
func main() {
for _, i := range smallPrimes {
fmt.Printf("The first 25 %d-smooth numbers are:\n", i)
fmt.Println(nSmooth(i, 25), "\n")
}
for _, i := range smallPrimes[1:] {
fmt.Printf("The 3,000th to 3,202nd %d-smooth numbers are:\n", i)
fmt.Println(nSmooth(i, 3002)[2999:], "\n")
}
for _, i := range []int{503, 509, 521} {
fmt.Printf("The 30,000th to 30,019th %d-smooth numbers are:\n", i)
fmt.Println(nSmooth(i, 30019)[29999:], "\n")
}
}
Output:
The first 25 2-smooth numbers are:
[1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 2097152 4194304 8388608 16777216] 

The first 25 3-smooth numbers are:
[1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 81 96 108 128 144 162 192] 

The first 25 5-smooth numbers are:
[1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 32 36 40 45 48 50 54] 

The first 25 7-smooth numbers are:
[1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36] 

The first 25 11-smooth numbers are:
[1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 18 20 21 22 24 25 27 28 30 32] 

The first 25 13-smooth numbers are:
[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 21 22 24 25 26 27 28] 

The first 25 17-smooth numbers are:
[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 24 25 26 27] 

The first 25 19-smooth numbers are:
[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 25 26] 

The first 25 23-smooth numbers are:
[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25] 

The first 25 29-smooth numbers are:
[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25] 

The 3,000th to 3,202nd 3-smooth numbers are:
[91580367978306252441724649472 92829823186414819915547541504 94096325042746502515294076928] 

The 3,000th to 3,202nd 5-smooth numbers are:
[278942752080 279936000000 281250000000] 

The 3,000th to 3,202nd 7-smooth numbers are:
[50176000 50331648 50388480] 

The 3,000th to 3,202nd 11-smooth numbers are:
[2112880 2116800 2117016] 

The 3,000th to 3,202nd 13-smooth numbers are:
[390000 390390 390625] 

The 3,000th to 3,202nd 17-smooth numbers are:
[145800 145860 146016] 

The 3,000th to 3,202nd 19-smooth numbers are:
[74256 74358 74360] 

The 3,000th to 3,202nd 23-smooth numbers are:
[46552 46575 46585] 

The 3,000th to 3,202nd 29-smooth numbers are:
[33516 33524 33534] 

The 30,000th to 30,019th 503-smooth numbers are:
[62913 62914 62916 62918 62920 62923 62926 62928 62930 62933 62935 62937 62944 62946 62951 62952 62953 62957 62959 62964] 

The 30,000th to 30,019th 509-smooth numbers are:
[62601 62602 62604 62607 62608 62609 62611 62618 62620 62622 62624 62625 62626 62628 62629 62634 62640 62643 62645 62646] 

The 30,000th to 30,019th 521-smooth numbers are:
[62287 62288 62291 62292 62300 62304 62307 62308 62310 62315 62320 62321 62322 62325 62328 62329 62330 62331 62335 62336] 

Julia[edit]

using Primes
 
function nsmooth(N, needed)
nexts, smooths = [BigInt(i) for i in 2:N if isprime(i)], [BigInt(1)]
prim, count = deepcopy(nexts), 1
indices = ones(Int, length(nexts))
while count < needed
x = minimum(nexts)
push!(smooths, x)
count += 1
for j in 1:length(nexts)
(nexts[j] <= x) && (nexts[j] = prim[j] * smooths[(indices[j] += 1)])
end
end
return (smooths[end] > typemax(Int)) ? smooths : Int.(smooths)
end
 
function testnsmoothfilters()
for i in filter(isprime, 1:29)
println("The first 25 n-smooth numbers for n = $i are: ", nsmooth(i, 25))
end
for i in filter(isprime, 3:29)
println("The 3000th through 3002nd ($i)-smooth numbers are: ", nsmooth(i, 3002)[3000:3002])
end
for i in filter(isprime, 503:521)
println("The 30000th through 30019th ($i)-smooth numbers >= 30000 are: ", nsmooth(i, 30019)[30000:30019])
end
end
 
testnsmoothfilters()
 
Output:
The first 25 n-smooth numbers for n = 2 are: [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216]
The first 25 n-smooth numbers for n = 3 are: [1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 128, 144, 162, 192]
The first 25 n-smooth numbers for n = 5 are: [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54]
The first 25 n-smooth numbers for n = 7 are: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36]
The first 25 n-smooth numbers for n = 11 are: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32]
The first 25 n-smooth numbers for n = 13 are: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28]
The first 25 n-smooth numbers for n = 17 are: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 27]
The first 25 n-smooth numbers for n = 19 are: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26]
The first 25 n-smooth numbers for n = 23 are: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]
The first 25 n-smooth numbers for n = 29 are: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]
The 3000th through 3002nd (3)-smooth numbers are: BigInt[91580367978306252441724649472, 92829823186414819915547541504, 94096325042746502515294076928]
The 3000th through 3002nd (5)-smooth numbers are: [278942752080, 279936000000, 281250000000]
The 3000th through 3002nd (7)-smooth numbers are: [50176000, 50331648, 50388480]
The 3000th through 3002nd (11)-smooth numbers are: [2112880, 2116800, 2117016]
The 3000th through 3002nd (13)-smooth numbers are: [390000, 390390, 390625]
The 3000th through 3002nd (17)-smooth numbers are: [145800, 145860, 146016]
The 3000th through 3002nd (19)-smooth numbers are: [74256, 74358, 74360]
The 3000th through 3002nd (23)-smooth numbers are: [46552, 46575, 46585]
The 3000th through 3002nd (29)-smooth numbers are: [33516, 33524, 33534]
The 30000th through 30019th (503)-smooth numbers >= 30000 are: [62913, 62914, 62916, 62918, 62920, 62923, 62926, 62928, 62930, 62933, 62935, 62937, 62944, 62946, 62951, 62952, 62953, 62957, 62959, 62964]
The 30000th through 30019th (509)-smooth numbers >= 30000 are: [62601, 62602, 62604, 62607, 62608, 62609, 62611, 62618, 62620, 62622, 62624, 62625, 62626, 62628, 62629, 62634, 62640, 62643, 62645, 62646]
The 30000th through 30019th (521)-smooth numbers >= 30000 are: [62287, 62288, 62291, 62292, 62300, 62304, 62307, 62308, 62310, 62315, 62320, 62321, 62322, 62325, 62328, 62329, 62330, 62331, 62335, 62336]

Kotlin[edit]

Translation of: Go
import java.math.BigInteger
 
var primes = mutableListOf<BigInteger>()
var smallPrimes = mutableListOf<Int>()
 
// cache all primes up to 521
fun init() {
val two = BigInteger.valueOf(2)
val three = BigInteger.valueOf(3)
val p521 = BigInteger.valueOf(521)
val p29 = BigInteger.valueOf(29)
primes.add(two)
smallPrimes.add(2)
var i = three
while (i <= p521) {
if (i.isProbablePrime(1)) {
primes.add(i)
if (i <= p29) {
smallPrimes.add(i.toInt())
}
}
i += two
}
}
 
fun min(bs: List<BigInteger>): BigInteger {
require(bs.isNotEmpty()) { "slice must have at lease one element" }
val it = bs.iterator()
var res = it.next()
while (it.hasNext()) {
val t = it.next()
if (t < res) {
res = t
}
}
return res
}
 
fun nSmooth(n: Int, size: Int): List<BigInteger> {
require(n in 2..521) { "n must be between 2 and 521" }
require(size >= 1) { "size must be at least 1" }
 
val bn = BigInteger.valueOf(n.toLong())
var ok = false
for (prime in primes) {
if (bn == prime) {
ok = true
break
}
}
require(ok) { "n must be a prime number" }
 
val ns = Array<BigInteger>(size) { BigInteger.ZERO }
ns[0] = BigInteger.ONE
val next = mutableListOf<BigInteger>()
for (i in 0 until primes.size) {
if (primes[i] > bn) {
break
}
next.add(primes[i])
}
val indices = Array(next.size) { 0 }
for (m in 1 until size) {
ns[m] = min(next)
for (i in indices.indices) {
if (ns[m] == next[i]) {
indices[i]++
next[i] = primes[i] * ns[indices[i]]
}
}
}
 
return ns.toList()
}
 
fun main() {
init()
for (i in smallPrimes) {
println("The first 25 $i-smooth numbers are:")
println(nSmooth(i, 25))
println()
}
for (i in smallPrimes.drop(1)) {
println("The 3,000th to 3,202 $i-smooth numbers are:")
println(nSmooth(i, 3_002).drop(2_999))
println()
}
for (i in listOf(503, 509, 521)) {
println("The 30,000th to 30,019 $i-smooth numbers are:")
println(nSmooth(i, 30_019).drop(29_999))
println()
}
}
Output:
The first 25 2-smooth numbers are:
[1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216]

The first 25 3-smooth numbers are:
[1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 128, 144, 162, 192]

The first 25 5-smooth numbers are:
[1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54]

The first 25 7-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36]

The first 25 11-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32]

The first 25 13-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28]

The first 25 17-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 27]

The first 25 19-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26]

The first 25 23-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]

The first 25 29-smooth numbers are:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]

The 3,000th to 3,202 3-smooth numbers are:
[91580367978306252441724649472, 92829823186414819915547541504, 94096325042746502515294076928]

The 3,000th to 3,202 5-smooth numbers are:
[278942752080, 279936000000, 281250000000]

The 3,000th to 3,202 7-smooth numbers are:
[50176000, 50331648, 50388480]

The 3,000th to 3,202 11-smooth numbers are:
[2112880, 2116800, 2117016]

The 3,000th to 3,202 13-smooth numbers are:
[390000, 390390, 390625]

The 3,000th to 3,202 17-smooth numbers are:
[145800, 145860, 146016]

The 3,000th to 3,202 19-smooth numbers are:
[74256, 74358, 74360]

The 3,000th to 3,202 23-smooth numbers are:
[46552, 46575, 46585]

The 3,000th to 3,202 29-smooth numbers are:
[33516, 33524, 33534]

The 30,000th to 30,019 503-smooth numbers are:
[62913, 62914, 62916, 62918, 62920, 62923, 62926, 62928, 62930, 62933, 62935, 62937, 62944, 62946, 62951, 62952, 62953, 62957, 62959, 62964]

The 30,000th to 30,019 509-smooth numbers are:
[62601, 62602, 62604, 62607, 62608, 62609, 62611, 62618, 62620, 62622, 62624, 62625, 62626, 62628, 62629, 62634, 62640, 62643, 62645, 62646]

The 30,000th to 30,019 521-smooth numbers are:
[62287, 62288, 62291, 62292, 62300, 62304, 62307, 62308, 62310, 62315, 62320, 62321, 62322, 62325, 62328, 62329, 62330, 62331, 62335, 62336]

Pascal[edit]

This example is incorrect. Please fix the code and remove this message.
Details:

for the 2nd part of the task,
starting at three thousand,
n-smooth for 3 and 5 aren't displayed.

Works with: Free Pascal
64-Bit.

Using trail-division with the first primes.Takes too long for first 3 after 2999 2,3,5-smooth numbers.

program HammNumb;
{$IFDEF FPC}
{$MODE DELPHI}
{$OPTIMIZATION ON,ALL}
{$ELSE}
{$APPTYPE CONSOLE}
{$ENDIF}
type
tHamNum = record
hampot : array[0..167] of Word;
hampotmax,
hamNum : NativeUint;
end;
 
const
primes : array[0..167] of word =
(2, 3, 5, 7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71
,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151
,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233
,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317
,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419
,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503
,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607
,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701
,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811
,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911
,919,929,937,941,947,953,967,971,977,983,991,997);
 
var
HNum:tHamNum;
 
procedure OutHamNum(const HNum:tHamNum);
var
i : NativeInt;
Begin
with Hnum do
Begin
write(hamNum:12,' : ');
For i := 0 to hampotmax-1 do
write(primes[i],'^',hampot[i],'*');
writeln(primes[hampotmax],'^',hampot[hampotmax]);
end;
end;
 
procedure NextHammNum(var HNum:tHamNum;maxP:NativeInt);
var
q,p,nr,n,pnum,momPrime : NativeUInt;
begin
n := HNum.hamNum;
repeat
inc(n);
nr := n;
//check divisibility by first (count=maxP) primes
pnum := 0;
repeat
momPrime := primes[pnum];
q := nr div momPrime;
p := 0;
while q*momPrime=nr do
Begin
inc(p);
nr := q;
q := nr div momPrime;
end;
HNum.hampot[pnum] := p;
inc(pnum);
until (nr=1) OR (pnum > maxp)
//finished ?
until nr = 1;
 
With HNum do
Begin
hamNum := n;
hamPotmax := pnum-1;
end;
end;
 
procedure OutXafterYSmooth(X,Y,SmoothIdx: NativeUInt);
var
i: NativeUint;
begin
IF SmoothIdx> High(primes) then
EXIT;
HNum.HamNum := 0;
dec(Y);
for i := 1 to Y do
NextHammNum(HNum,SmoothIdx);
write('first ',X,' after ',Y,' ',primes[SmoothIdx]:3,'-smooth numbers : ');
for i := 1 to X do
begin
NextHammNum(HNum,SmoothIdx);
write(HNum.HamNum,' ');
end;
writeln;
end;
 
var
j: NativeUint;
Begin
j := 0;
while primes[j] <= 29 do
Begin
OutXafterYSmooth(25,1,j);
inc(j);
end;
writeln;
 
j := 3;
while primes[j] <= 29 do
Begin
OutXafterYSmooth(3,3000,j);
inc(j);
end;
writeln;
while primes[j] < 503 do
inc(j);
while primes[j] <= 521 do
Begin
OutXafterYSmooth(20,30000,j);
inc(j);
end;
writeln;
End.
Output:
first 25 after 0   2-smooth numbers : 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 2097152 4194304 8388608 16777216

first 25 after 0 3-smooth numbers : 1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 81 96 108 128 144 162 192 first 25 after 0 5-smooth numbers : 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 32 36 40 45 48 50 54 first 25 after 0 7-smooth numbers : 1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36 first 25 after 0 11-smooth numbers : 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 18 20 21 22 24 25 27 28 30 32 first 25 after 0 13-smooth numbers : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 21 22 24 25 26 27 28 first 25 after 0 17-smooth numbers : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 24 25 26 27 first 25 after 0 19-smooth numbers : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 25 26 first 25 after 0 23-smooth numbers : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 first 25 after 0 29-smooth numbers : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

first 3 after 2999 7-smooth numbers : 50176000 50331648 50388480 first 3 after 2999 11-smooth numbers : 2112880 2116800 2117016 first 3 after 2999 13-smooth numbers : 390000 390390 390625 first 3 after 2999 17-smooth numbers : 145800 145860 146016 first 3 after 2999 19-smooth numbers : 74256 74358 74360 first 3 after 2999 23-smooth numbers : 46552 46575 46585 first 3 after 2999 29-smooth numbers : 33516 33524 33534

first 20 after 29999 503-smooth numbers : 62913 62914 62916 62918 62920 62923 62926 62928 62930 62933 62935 62937 62944 62946 62951 62952 62953 62957 62959 62964 first 20 after 29999 509-smooth numbers : 62601 62602 62604 62607 62608 62609 62611 62618 62620 62622 62624 62625 62626 62628 62629 62634 62640 62643 62645 62646 first 20 after 29999 521-smooth numbers : 62287 62288 62291 62292 62300 62304 62307 62308 62310 62315 62320 62321 62322 62325 62328 62329 62330 62331 62335 62336

real 0m2,665s user 0m2,655s sys 0m0,003s

Perl[edit]

Library: ntheory
use strict;
use warnings;
use feature 'say';
use ntheory qw<primes>;
use List::Util qw<min>;
 
#use bigint # works, but slow
use Math::GMPz; # this module gives roughly 16x speed-up
 
sub smooth_numbers {
# my(@m) = @_; # use with 'bigint'
my @m = map { Math::GMPz->new($_) } @_; # comment out to NOT use Math::GMPz
my @s;
push @s, [1] for 0..$#m;
 
return sub {
my $n = $s[0][0];
$n = min $n, $s[$_][0] for 1..$#m;
for (0..$#m) {
shift @{$s[$_]} if $s[$_][0] == $n;
push @{$s[$_]}, $n * $m[$_]
}
return $n
}
}
 
sub abbrev {
my($n) = @_;
return $n if length($n) <= 50;
substr($n,0,10) . "...(@{[length($n) - 2*10]} digits omitted)..." . substr($n, -10, 10)
}
 
my @primes = @{primes(10_000)};
 
my $start = 3000; my $cnt = 3;
for my $n_smooth (0..9) {
say "\nFirst 25, and ${start}th through @{[$start+2]}nd $primes[$n_smooth]-smooth numbers:";
my $s = smooth_numbers(@primes[0..$n_smooth]);
my @S25;
push @S25, $s->() for 1..25;
say join ' ', @S25;
 
my @Sm; my $c = 25;
do {
my $sn = $s->();
push @Sm, abbrev($sn) if ++$c >= $start;
} until @Sm == $cnt;
say join ' ', @Sm;
}
 
$start = 30000; $cnt = 20;
for my $n_smooth (95..97) { # (503, 509, 521) {
say "\n${start}th through @{[$start+$cnt-1]}th $primes[$n_smooth]-smooth numbers:";
my $s = smooth_numbers(@primes[0..$n_smooth]);
my(@Sm,$c);
do {
my $sn = $s->();
push @Sm, $sn if ++$c >= $start;
} until @Sm == $cnt;
say join ' ', @Sm;
}
Output:
First 25, and 3000th through 3002nd 2-smooth numbers:
1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 2097152 4194304 8388608 16777216
6151159610...(883 digits omitted)...9114994688 1230231922...(884 digits omitted)...8229989376 2460463844...(884 digits omitted)...6459978752

First 25, and 3000th through 3002nd 3-smooth numbers:
1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 81 96 108 128 144 162 192
91580367978306252441724649472 92829823186414819915547541504 94096325042746502515294076928

First 25, and 3000th through 3002nd 5-smooth numbers:
1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 32 36 40 45 48 50 54
278942752080 279936000000 281250000000

First 25, and 3000th through 3002nd 7-smooth numbers:
1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36
50176000 50331648 50388480

First 25, and 3000th through 3002nd 11-smooth numbers:
1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 18 20 21 22 24 25 27 28 30 32
2112880 2116800 2117016

First 25, and 3000th through 3002nd 13-smooth numbers:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 21 22 24 25 26 27 28
390000 390390 390625

First 25, and 3000th through 3002nd 17-smooth numbers:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 24 25 26 27
145800 145860 146016

First 25, and 3000th through 3002nd 19-smooth numbers:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 25 26
74256 74358 74360

First 25, and 3000th through 3002nd 23-smooth numbers:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
46552 46575 46585

First 25, and 3000th through 3002nd 29-smooth numbers:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
33516 33524 33534

30000th through 30019th 503-smooth numbers:
62913 62914 62916 62918 62920 62923 62926 62928 62930 62933 62935 62937 62944 62946 62951 62952 62953 62957 62959 62964

30000th through 30019th 509-smooth numbers:
62601 62602 62604 62607 62608 62609 62611 62618 62620 62622 62624 62625 62626 62628 62629 62634 62640 62643 62645 62646

30000th through 30019th 521-smooth numbers:
62287 62288 62291 62292 62300 62304 62307 62308 62310 62315 62320 62321 62322 62325 62328 62329 62330 62331 62335 62336

Perl 6[edit]

Works with: Rakudo version 2019.07.1
sub smooth-numbers (*@list) {
cache my \Smooth := gather {
my %i = (flat @list) Z=> (Smooth.iterator for ^@list);
my %n = (flat @list) Z=> 1 xx *;
 
loop {
take my $n := %n{*}.min;
 
for @list -> \k {
%n{k} = %i{k}.pull-one * k if %n{k} == $n;
}
}
}
}
 
sub abbrev ($n) {
$n.chars > 50 ??
$n.substr(0,10) ~ "...({$n.chars - 20} digits omitted)..." ~ $n.substr(* - 10) !!
$n
}
 
my @primes = (2..*).grep: *.is-prime;
 
my $start = 3000;
 
for ^@primes.first( * > 29, :k ) -> $p {
put join "\n", "\nFirst 25, and {$start}th through {$start+2}nd {@primes[$p]}-smooth numbers:",
$(smooth-numbers(|@primes[0..$p])[^25]),
$(smooth-numbers(|@primes[0..$p])[$start - 1 .. $start + 1]».&abbrev);
}
 
$start = 30000;
 
for 503, 509, 521 -> $p {
my $i = @primes.first( * == $p, :k );
put "\n{$start}th through {$start+19}th {@primes[$i]}-smooth numbers:\n" ~
smooth-numbers(|@primes[0..$i])[$start - 1 .. $start + 18];
}
Output:
First 25, and 3000th through 3002nd 2-smooth numbers:
1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 2097152 4194304 8388608 16777216
6151159610...(883 digits omitted)...9114994688 1230231922...(884 digits omitted)...8229989376 2460463844...(884 digits omitted)...6459978752

First 25, and 3000th through 3002nd 3-smooth numbers:
1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 81 96 108 128 144 162 192
91580367978306252441724649472 92829823186414819915547541504 94096325042746502515294076928

First 25, and 3000th through 3002nd 5-smooth numbers:
1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 32 36 40 45 48 50 54
278942752080 279936000000 281250000000

First 25, and 3000th through 3002nd 7-smooth numbers:
1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36
50176000 50331648 50388480

First 25, and 3000th through 3002nd 11-smooth numbers:
1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 18 20 21 22 24 25 27 28 30 32
2112880 2116800 2117016

First 25, and 3000th through 3002nd 13-smooth numbers:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 21 22 24 25 26 27 28
390000 390390 390625

First 25, and 3000th through 3002nd 17-smooth numbers:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 24 25 26 27
145800 145860 146016

First 25, and 3000th through 3002nd 19-smooth numbers:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 25 26
74256 74358 74360

First 25, and 3000th through 3002nd 23-smooth numbers:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
46552 46575 46585

First 25, and 3000th through 3002nd 29-smooth numbers:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
33516 33524 33534

30000th through 30019th 503-smooth numbers:
62913 62914 62916 62918 62920 62923 62926 62928 62930 62933 62935 62937 62944 62946 62951 62952 62953 62957 62959 62964

30000th through 30019th 509-smooth numbers:
62601 62602 62604 62607 62608 62609 62611 62618 62620 62622 62624 62625 62626 62628 62629 62634 62640 62643 62645 62646

30000th through 30019th 521-smooth numbers:
62287 62288 62291 62292 62300 62304 62307 62308 62310 62315 62320 62321 62322 62325 62328 62329 62330 62331 62335 62336

Phix[edit]

Library: mpfr
Translation of: Julia
include mpfr.e
 
function nsmooth(integer n, integer needed)
-- note that n is a prime index, ie 1,2,3,4... for 2,3,5,7...
sequence smooth = {mpz_init(1)},
nexts = get_primes(-n),
indices = repeat(1,n)
for i=1 to n do nexts[i] = mpz_init(nexts[i]) end for
for i=2 to needed do
mpz x = mpz_init_set(mpz_min(nexts))
smooth = append(smooth,x)
for j=1 to n do
if mpz_cmp(nexts[j],x)<=0 then
indices[j] += 1
mpz_mul_si(nexts[j],smooth[indices[j]],get_prime(j))
end if
end for
end for
return smooth
end function
 
function flat_str(sequence s)
for i=1 to length(s) do s[i] = shorten(mpz_get_str(s[i]),ml:=10) end for
return join(s," ")
end function
 
for n=1 to 10 do
printf(1,"%d-smooth[1..25]: %s\n",{get_prime(n),flat_str(nsmooth(n, 25))})
end for
for n=1 to 10 do
printf(1,"%d-smooth[3000..3002]: %s\n",{get_prime(n),flat_str(nsmooth(n, 3002)[3000..3002])})
end for
for n=96 to 98 do -- primes 503, 509, and 521
printf(1,"%d-smooth[30000..30019]: %s\n",{get_prime(n),flat_str(nsmooth(n, 30019)[30000..30019])})
end for
Output:
2-smooth[1..25]: 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 2097152 4194304 8388608 16777216
3-smooth[1..25]: 1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 81 96 108 128 144 162 192
5-smooth[1..25]: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 32 36 40 45 48 50 54
7-smooth[1..25]: 1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36
11-smooth[1..25]: 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 18 20 21 22 24 25 27 28 30 32
13-smooth[1..25]: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 21 22 24 25 26 27 28
17-smooth[1..25]: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 24 25 26 27
19-smooth[1..25]: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 25 26
23-smooth[1..25]: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
29-smooth[1..25]: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
2-smooth[3000..3002]: 615115961...114994688 (903 digits) 123023192...229989376 (904 digits) 246046384...459978752 (904 digits)
3-smooth[3000..3002]: 91580367978306252441724649472 92829823186414819915547541504 94096325042746502515294076928
5-smooth[3000..3002]: 278942752080 279936000000 281250000000
7-smooth[3000..3002]: 50176000 50331648 50388480
11-smooth[3000..3002]: 2112880 2116800 2117016
13-smooth[3000..3002]: 390000 390390 390625
17-smooth[3000..3002]: 145800 145860 146016
19-smooth[3000..3002]: 74256 74358 74360
23-smooth[3000..3002]: 46552 46575 46585
29-smooth[3000..3002]: 33516 33524 33534
503-smooth[30000..30019]: 62913 62914 62916 62918 62920 62923 62926 62928 62930 62933 62935 62937 62944 62946 62951 62952 62953 62957 62959 62964
509-smooth[30000..30019]: 62601 62602 62604 62607 62608 62609 62611 62618 62620 62622 62624 62625 62626 62628 62629 62634 62640 62643 62645 62646
521-smooth[30000..30019]: 62287 62288 62291 62292 62300 62304 62307 62308 62310 62315 62320 62321 62322 62325 62328 62329 62330 62331 62335 62336

REXX[edit]

/*REXX pgm computes&displays X n-smooth numbers; both X and N can be specified as ranges*/
numeric digits 200 /*be able to handle some big numbers. */
parse arg LOx HIx LOn HIn . /*obtain optional arguments from the CL*/
if LOx=='' | LOx=="," then LOx= 1 /*Not specified? Then use the default.*/
if HIx=='' | HIx=="," then HIx= LOx + 24 /* " " " " " " */
if LOn=='' | LOn=="," then LOn= 2 /* " " " " " " */
if HIn=='' | HIn=="," then HIn= LOn + 27 /* " " " " " " */
call genP HIn /*generate enough primes to satisfy HIn*/
@aList= ' a list of the '; @thru= ' through ' /*literals used with a SAY.*/
 
do j=LOn to HIn; if !.j==0 then iterate /*if not prime, then skip this number. */
call smooth HIx,j; $= /*invoke SMOOTH; initialize $ (list). */
do k=LOx to HIx; $= $ #.k /*append a smooth number to " " " */
end /*k*/
say center(@aList th(LOx) @thru th(HIx) ' numbers for' j"-smooth ", 130, "═")
say strip($); say
end /*j*/ /* [↑] the $ list has a leading blank.*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
genP: procedure expose @. !. #; parse arg x /*#≡num of primes; @. ≡array of primes.*/
@.=; @.1=2; @.2=3; @.3=5; @.4=7; @.5=11; @.6=13; @.7=17; @.8=19; @.9=23; #=9
 !.=0;  !.2=1; !.3=2; !.5=3; !.7=4; !.11=5; !.13=6; !.17=7; !.19=8; !.23=9
do [email protected].#+6 by 2 until #>=x ; if k//3==0 then iterate
parse var k '' -1 _; if _==5 then iterate
do d=4 until @.d**2>k; if k//@.d==0 then iterate k
end /*d*/
#= # + 1;  !.k= #; @.#= k /*found a prime, bump counter; assign @*/
end /*k*/; return
/*──────────────────────────────────────────────────────────────────────────────────────*/
smooth: procedure expose @. !. #.; parse arg y,p /*obtain the arguments from the invoker*/
if p=='' then p= 3 /*Not specified? Then assume Hamming #s*/
n= !.p /*the number of primes being used. */
nn= n - 1; #.= 0; #.1= 1 /*an array of n-smooth numbers (so far)*/
f.= 1 /*the indices of factors of a number. */
do j=2 for y-1; _= f.1
z= @.1 * #._
do k=2 for nn; _= f.k; v= @.k * #._; if v<z then z= v
end /*k*/
#.j= z
do d=1 for n; _= f.d; if @.d * #._==z then f.d= f.d + 1
end /*d*/
end /*j*/; return
/*──────────────────────────────────────────────────────────────────────────────────────*/
th: parse arg th; return th || word('th st nd rd', 1+(th//10)*(th//100%10\==1)*(th//10<4))
output   when using the default inputs:
════════════════════════════════════ a list of the  1st  through  25th  numbers for 2-smooth ═════════════════════════════════════
1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 2097152 4194304 8388608 16777216

════════════════════════════════════ a list of the  1st  through  25th  numbers for 3-smooth ═════════════════════════════════════
1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 81 96 108 128 144 162 192

════════════════════════════════════ a list of the  1st  through  25th  numbers for 5-smooth ═════════════════════════════════════
1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 32 36 40 45 48 50 54

════════════════════════════════════ a list of the  1st  through  25th  numbers for 7-smooth ═════════════════════════════════════
1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36

════════════════════════════════════ a list of the  1st  through  25th  numbers for 11-smooth ════════════════════════════════════
1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 18 20 21 22 24 25 27 28 30 32

════════════════════════════════════ a list of the  1st  through  25th  numbers for 13-smooth ════════════════════════════════════
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 21 22 24 25 26 27 28

════════════════════════════════════ a list of the  1st  through  25th  numbers for 17-smooth ════════════════════════════════════
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 24 25 26 27

════════════════════════════════════ a list of the  1st  through  25th  numbers for 19-smooth ════════════════════════════════════
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 25 26

════════════════════════════════════ a list of the  1st  through  25th  numbers for 23-smooth ════════════════════════════════════
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

════════════════════════════════════ a list of the  1st  through  25th  numbers for 29-smooth ════════════════════════════════════
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
output   when using the input of:     3000   3002   3   29
══════════════════════════════════ a list of the  3000th  through  3002nd  numbers for 3-smooth ══════════════════════════════════
91580367978306252441724649472 92829823186414819915547541504 94096325042746502515294076928

══════════════════════════════════ a list of the  3000th  through  3002nd  numbers for 5-smooth ══════════════════════════════════
278942752080 279936000000 281250000000

══════════════════════════════════ a list of the  3000th  through  3002nd  numbers for 7-smooth ══════════════════════════════════
50176000 50331648 50388480

═════════════════════════════════ a list of the  3000th  through  3002nd  numbers for 11-smooth ══════════════════════════════════
2112880 2116800 2117016

═════════════════════════════════ a list of the  3000th  through  3002nd  numbers for 13-smooth ══════════════════════════════════
390000 390390 390625

═════════════════════════════════ a list of the  3000th  through  3002nd  numbers for 17-smooth ══════════════════════════════════
145800 145860 146016

═════════════════════════════════ a list of the  3000th  through  3002nd  numbers for 19-smooth ══════════════════════════════════
74256 74358 74360

═════════════════════════════════ a list of the  3000th  through  3002nd  numbers for 23-smooth ══════════════════════════════════
46552 46575 46585

═════════════════════════════════ a list of the  3000th  through  3002nd  numbers for 29-smooth ══════════════════════════════════
33516 33524 33534
output   when using the input of:     30000   30019   503   521
════════════════════════════════ a list of the  30000th  through  30019th  numbers for 503-smooth ════════════════════════════════
62913 62914 62916 62918 62920 62923 62926 62928 62930 62933 62935 62937 62944 62946 62951 62952 62953 62957 62959 62964

════════════════════════════════ a list of the  30000th  through  30019th  numbers for 509-smooth ════════════════════════════════
62601 62602 62604 62607 62608 62609 62611 62618 62620 62622 62624 62625 62626 62628 62629 62634 62640 62643 62645 62646

════════════════════════════════ a list of the  30000th  through  30019th  numbers for 521-smooth ════════════════════════════════
62287 62288 62291 62292 62300 62304 62307 62308 62310 62315 62320 62321 62322 62325 62328 62329 62330 62331 62335 62336

Sidef[edit]

func smooth_generator(primes) {
var s = primes.len.of { [1] }
{
var n = s.map { .first }.min
{ |i|
s[i].shift if (s[i][0] == n)
s[i] << (n * primes[i])
} * primes.len
n
}
}
 
for p in (primes(2,29)) {
var g = smooth_generator(p.primes)
say ("First 25 #{'%2d'%p}-smooth numbers: ", 25.of { g.run }.join(' '))
}
 
say ''
 
for p in (primes(3,29)) {
var g = smooth_generator(p.primes)
say ("3,000th through 3,002nd #{'%2d'%p}-smooth numbers: ", 3002.of { g.run }.last(3).join(' '))
}
Output:
First 25  2-smooth numbers: 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 2097152 4194304 8388608 16777216
First 25  3-smooth numbers: 1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 81 96 108 128 144 162 192
First 25  5-smooth numbers: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 32 36 40 45 48 50 54
First 25  7-smooth numbers: 1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36
First 25 11-smooth numbers: 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 18 20 21 22 24 25 27 28 30 32
First 25 13-smooth numbers: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 21 22 24 25 26 27 28
First 25 17-smooth numbers: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 24 25 26 27
First 25 19-smooth numbers: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 25 26
First 25 23-smooth numbers: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
First 25 29-smooth numbers: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

3,000th through 3,002nd  3-smooth numbers: 91580367978306252441724649472 92829823186414819915547541504 94096325042746502515294076928
3,000th through 3,002nd  5-smooth numbers: 278942752080 279936000000 281250000000
3,000th through 3,002nd  7-smooth numbers: 50176000 50331648 50388480
3,000th through 3,002nd 11-smooth numbers: 2112880 2116800 2117016
3,000th through 3,002nd 13-smooth numbers: 390000 390390 390625
3,000th through 3,002nd 17-smooth numbers: 145800 145860 146016
3,000th through 3,002nd 19-smooth numbers: 74256 74358 74360
3,000th through 3,002nd 23-smooth numbers: 46552 46575 46585
3,000th through 3,002nd 29-smooth numbers: 33516 33524 33534

Optionally, an efficient algorithm for checking if a given arbitrary large number is smooth over a given product of primes:

func is_smooth_over_prod(n, k) {
 
return true if (n == 1)
return false if (n <= 0)
 
for (var g = gcd(n,k); g > 1; g = gcd(n,k)) {
n /= g**valuation(n,g) # remove any divisibility by g
return true if (n == 1) # smooth if n == 1
}
 
return false
}
 
for p in (503, 509, 521) {
var k = p.primorial
var a = {|n| is_smooth_over_prod(n, k) }.first(30_019).last(20)
say ("30,000th through 30,019th #{p}-smooth numbers: ", a.join(' '))
}
Output:
30,000th through 30,019th 503-smooth numbers: 62913 62914 62916 62918 62920 62923 62926 62928 62930 62933 62935 62937 62944 62946 62951 62952 62953 62957 62959 62964
30,000th through 30,019th 509-smooth numbers: 62601 62602 62604 62607 62608 62609 62611 62618 62620 62622 62624 62625 62626 62628 62629 62634 62640 62643 62645 62646
30,000th through 30,019th 521-smooth numbers: 62287 62288 62291 62292 62300 62304 62307 62308 62310 62315 62320 62321 62322 62325 62328 62329 62330 62331 62335 62336

Swift[edit]

import BigInt
import Foundation
 
extension BinaryInteger {
@inlinable
public var isPrime: Bool {
if self == 0 || self == 1 {
return false
} else if self == 2 {
return true
}
 
let max = Self(ceil((Double(self).squareRoot())))
 
for i in stride(from: 2, through: max, by: 1) {
if self % i == 0 {
return false
}
}
 
return true
}
}
 
@inlinable
public func smoothN<T: BinaryInteger>(n: T, count: Int) -> [T] {
let primes = stride(from: 2, to: n + 1, by: 1).filter({ $0.isPrime })
var next = primes
var indices = [Int](repeating: 0, count: primes.count)
var res = [T](repeating: 0, count: count)
 
res[0] = 1
 
guard count > 1 else {
return res
}
 
for m in 1..<count {
res[m] = next.min()!
 
for i in 0..<indices.count where res[m] == next[i] {
indices[i] += 1
next[i] = primes[i] * res[indices[i]]
}
}
 
return res
}
 
for n in 2...29 where n.isPrime {
print("The first 25 \(n)-smooth numbers are: \(smoothN(n: n, count: 25))")
}
 
print()
 
for n in 3...29 where n.isPrime {
print("The 3000...3002 \(n)-smooth numbers are: \(smoothN(n: BigInt(n), count: 3002).dropFirst(2999).prefix(3))")
}
 
print()
 
for n in 503...521 where n.isPrime {
print("The 30,000...30,019 \(n)-smooth numbers are: \(smoothN(n: BigInt(n), count: 30_019).dropFirst(29999).prefix(20))")
}
Output:
The first 25 2-smooth numbers are: [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216]
The first 25 3-smooth numbers are: [1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 128, 144, 162, 192]
The first 25 5-smooth numbers are: [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54]
The first 25 7-smooth numbers are: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36]
The first 25 11-smooth numbers are: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32]
The first 25 13-smooth numbers are: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28]
The first 25 17-smooth numbers are: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 27]
The first 25 19-smooth numbers are: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26]
The first 25 23-smooth numbers are: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]
The first 25 29-smooth numbers are: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]

The 3000...3002 3-smooth numbers are: [91580367978306252441724649472, 92829823186414819915547541504, 94096325042746502515294076928]
The 3000...3002 5-smooth numbers are: [278942752080, 279936000000, 281250000000]
The 3000...3002 7-smooth numbers are: [50176000, 50331648, 50388480]
The 3000...3002 11-smooth numbers are: [2112880, 2116800, 2117016]
The 3000...3002 13-smooth numbers are: [390000, 390390, 390625]
The 3000...3002 17-smooth numbers are: [145800, 145860, 146016]
The 3000...3002 19-smooth numbers are: [74256, 74358, 74360]
The 3000...3002 23-smooth numbers are: [46552, 46575, 46585]
The 3000...3002 29-smooth numbers are: [33516, 33524, 33534]

The 30,000...30,019 503-smooth numbers are: [62913, 62914, 62916, 62918, 62920, 62923, 62926, 62928, 62930, 62933, 62935, 62937, 62944, 62946, 62951, 62952, 62953, 62957, 62959, 62964]
The 30,000...30,019 509-smooth numbers are: [62601, 62602, 62604, 62607, 62608, 62609, 62611, 62618, 62620, 62622, 62624, 62625, 62626, 62628, 62629, 62634, 62640, 62643, 62645, 62646]
The 30,000...30,019 521-smooth numbers are: [62287, 62288, 62291, 62292, 62300, 62304, 62307, 62308, 62310, 62315, 62320, 62321, 62322, 62325, 62328, 62329, 62330, 62331, 62335, 62336]

zkl[edit]

Translation of: Go
Library: GMP
GNU Multiple Precision Arithmetic Library and primes
var [const] BI=Import("zklBigNum");  // libGMP
 
fcn nSmooth(n,sz){ // --> List of big ints
if(sz<1) throw(Exception.ValueError("size must be at least 1"));
bn,primes,ns := BI(n), List(), List.createLong(sz);
if(not bn.probablyPrime()) throw(Exception.ValueError("n must be prime"));
p:=BI(1); while(p<n){ primes.append(p.nextPrime().copy()) } // includes n
ns.append(BI(1));
next:=primes.copy();
if(Void!=( z:=primes.find(bn)) ) next.del(z+1,*);
 
indices:=List.createLong(next.len(),0);
do(sz-1){
ns.append( nm:=BI( next.reduce(fcn(a,b){ a.min(b) }) ));
foreach i in (indices.len()){
if(nm==next[i]){
indices[i]+=1;
next[i]=primes[i]*ns[indices[i]];
}
}
}
ns
}
smallPrimes:=List();
p:=BI(1); while(p<29) { smallPrimes.append(p.nextPrime().toInt()) }
 
foreach p in (smallPrimes){
println("The first 25 %d-smooth numbers are:".fmt(p));
println(nSmooth(p,25).concat(" "), "\n")
}
foreach p in (smallPrimes[1,*]){
print("The 3,000th to 3,202nd %d-smooth numbers are: ".fmt(p));
println(nSmooth(p,3002)[2999,*].concat(" "));
}
foreach p in (T(503,509,521)){
println("\nThe 30,000th to 30,019th %d-smooth numbers are:".fmt(p));
println(nSmooth(p,30019)[29999,*].concat(" "));
}
Output:
The first 25 2-smooth numbers are:
1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 2097152 4194304 8388608 16777216

The first 25 3-smooth numbers are:
1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 81 96 108 128 144 162 192

The first 25 5-smooth numbers are:
1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 32 36 40 45 48 50 54

The first 25 7-smooth numbers are:
1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36

The first 25 11-smooth numbers are:
1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 18 20 21 22 24 25 27 28 30 32

The first 25 13-smooth numbers are:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 20 21 22 24 25 26 27 28

The first 25 17-smooth numbers are:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 24 25 26 27

The first 25 19-smooth numbers are:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 25 26

The first 25 23-smooth numbers are:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

The first 25 29-smooth numbers are:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

The 3,000th to 3,202nd 3-smooth numbers are: 91580367978306252441724649472 92829823186414819915547541504 94096325042746502515294076928
The 3,000th to 3,202nd 5-smooth numbers are: 278942752080 279936000000 281250000000
The 3,000th to 3,202nd 7-smooth numbers are: 50176000 50331648 50388480
The 3,000th to 3,202nd 11-smooth numbers are: 2112880 2116800 2117016
The 3,000th to 3,202nd 13-smooth numbers are: 390000 390390 390625
The 3,000th to 3,202nd 17-smooth numbers are: 145800 145860 146016
The 3,000th to 3,202nd 19-smooth numbers are: 74256 74358 74360
The 3,000th to 3,202nd 23-smooth numbers are: 46552 46575 46585
The 3,000th to 3,202nd 29-smooth numbers are: 33516 33524 33534

The 30,000th to 30,019th 503-smooth numbers are:
62913 62914 62916 62918 62920 62923 62926 62928 62930 62933 62935 62937 62944 62946 62951 62952 62953 62957 62959 62964

The 30,000th to 30,019th 509-smooth numbers are:
62601 62602 62604 62607 62608 62609 62611 62618 62620 62622 62624 62625 62626 62628 62629 62634 62640 62643 62645 62646

The 30,000th to 30,019th 521-smooth numbers are:
62287 62288 62291 62292 62300 62304 62307 62308 62310 62315 62320 62321 62322 62325 62328 62329 62330 62331 62335 62336