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Ingy döt Net 2026-04-30 12:34:36 -04:00
parent 4bb20c9b71
commit cbaf4c4b64
12390 changed files with 318560 additions and 27248 deletions
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35
Task/Aliquot-sequence-classifications/Crystal/aliquot-sequence-classifications.cr Normal file
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def sum_proper_divisors (n)
z = n.class.zero
(z+1..n//2).sum(z) {|i| n % i == 0 ? i : 0 }
end
def aliquot (n)
seq = [n]
limit = 2_i64**47
15.times do
n = sum_proper_divisors(n)
case n
when 0 then return { "terminating", seq << n }
when .>(limit) then return { "non-terminating", seq << n }
when seq[0] then return { case seq.size
when 1 then "perfect"
when 2 then "amicable"
else "sociable"
end, seq }
when seq.last then return { "aspiring", seq }
when .in?(seq) then return { "cyclic", seq << n }
end
seq << n
end
{ "non-terminating", seq }
end
(1..10).each do |i|
kind, seq = aliquot(i)
puts "%s: %s" % { kind, seq }
end
puts
[11, 12, 28, 496, 220, 1184, 12496, 1264460, 790, 909, 562, 1064, 1488].each do |i|
kind, seq = aliquot(i)
puts "%s: %s" % { kind, seq }
end

56
Task/Aliquot-sequence-classifications/Pluto/aliquot-sequence-classifications.pluto Normal file
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local int = require "int"
local fmt = require "fmt"
require "table2"
$define THRESHOLD = 1 << 47
class classification
function __construct(public seq, public aliquot) end
end
local function classify_sequence(k)
assert(k > 0, "K must be positive")
local last = k
local seq = {k}
while true do
last = int.divisors(last, true):sum()
seq:insert(last)
local n = #seq
local aliquot = ""
if last == 0 then
aliquot = "Terminating"
elseif n == 2 and last == k then
aliquot = "Perfect"
elseif n == 3 and last == k then
aliquot = "Amicable"
elseif n >= 4 and last == k then
aliquot = $"Sociable[{n - 1}]"
elseif last == seq[n - 1] then
aliquot = "Aspiring"
elseif n > 3 and (last in seq:slice(2, n - 2)) then
local ix = seq:findindex(|e| -> e == last) ?? -1
aliquot = $"Cyclic[{n - ix}]"
elseif n == 16 or last > THRESHOLD then
aliquot = "Non-terminating"
end
if aliquot != "" then return new classification(seq, aliquot) end
end
end
print("Aliquot classifications - periods for Sociable/Cyclic in square brackets:\n")
for k = 1, 10 do
local c = classify_sequence(k)
fmt.print("%2d: %-15s %,s", k, c.aliquot, c.seq)
end
print()
local a = {11, 12, 28, 496, 220, 1184, 12496, 1264460, 790, 909, 562, 1064, 1488}
for a as k do
local c = classify_sequence(k)
fmt.print("%7d: %-15s %,s", k, c.aliquot, c.seq)
end
print()
local k = 15355717786080
local c = classify_sequence(k)
fmt.print("%d: %-15s %,s", k, c.aliquot, c.seq)

34
Task/Aliquot-sequence-classifications/PowerShell/aliquot-sequence-classifications-1.ps1 Normal file
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function Get-NextAliquot ( [int]$X )
{
If ( $X -gt 1 )
{
$NextAliquot = 0
(1..($X/2)).Where{ $x % $_ -eq 0 }.ForEach{ $NextAliquot += $_ }.Where{ $_ }
return $NextAliquot
}
}
function Get-AliquotSequence ( [int]$K, [int]$N )
{
$X = $K
$X
(1..($N-1)).ForEach{ $X = Get-NextAliquot $X; $X }
}
function Classify-AlliquotSequence ( [int[]]$Sequence )
{
$K = $Sequence[0]
$LastN = $Sequence.Count
If ( $Sequence[-1] -eq 0 ) { return "terminating" }
If ( $Sequence[-1] -eq 1 ) { return "terminating" }
If ( $Sequence[1] -eq $K ) { return "perfect" }
If ( $Sequence[2] -eq $K ) { return "amicable" }
If ( $Sequence[3..($Sequence.Count-1)] -contains $K ) { return "sociable" }
If ( $Sequence[-1] -eq $Sequence[-2] ) { return "aspiring" }
If ( $Sequence.Count -gt ( $Sequence | Select -Unique ).Count ) { return "cyclic" }
return "non-terminating and non-repeating through N = $($Sequence.Count)"
}
(1..10).ForEach{ [string]$_ + " is " + ( Classify-AlliquotSequence -Sequence ( Get-AliquotSequence -K $_ -N 16 ) ) }
( 11, 12, 28, 496, 220, 1184, 790, 909, 562, 1064, 1488 ).ForEach{ [string]$_ + " is " + ( Classify-AlliquotSequence -Sequence ( Get-AliquotSequence -K $_ -N 16 ) ) }

63
Task/Aliquot-sequence-classifications/PowerShell/aliquot-sequence-classifications-2.ps1 Normal file
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function Get-NextAliquot ( [int]$X )
{
If ( $X -gt 1 )
{
$NextAliquot = 1
If ( $X -gt 2 )
{
$XSquareRoot = [math]::Sqrt( $X )
(2..$XSquareRoot).Where{ $X % $_ -eq 0 }.ForEach{ $NextAliquot += $_ + $x / $_ }
If ( $XSquareRoot % 1 -eq 0 ) { $NextAliquot -= $XSquareRoot }
}
return $NextAliquot
}
}
function Get-AliquotSequence ( [int]$K, [int]$N )
{
$X = $K
$X
$i = 1
While ( $X -and $i -lt $N )
{
$i++
$Next = Get-NextAliquot $X
If ( $Next )
{
If ( $X -eq $Next )
{
($i..$N).ForEach{ $X }
$i = $N
}
Else
{
$X = $Next
$X
}
}
Else
{
$i = $N
}
}
}
function Classify-AlliquotSequence ( [int[]]$Sequence )
{
$K = $Sequence[0]
$LastN = $Sequence.Count
If ( $Sequence[-1] -eq 0 ) { return "terminating" }
If ( $Sequence[-1] -eq 1 ) { return "terminating" }
If ( $Sequence[1] -eq $K ) { return "perfect" }
If ( $Sequence[2] -eq $K ) { return "amicable" }
If ( $Sequence[3..($Sequence.Count-1)] -contains $K ) { return "sociable" }
If ( $Sequence[-1] -eq $Sequence[-2] ) { return "aspiring" }
If ( $Sequence.Count -gt ( $Sequence | Select -Unique ).Count ) { return "cyclic" }
return "non-terminating and non-repeating through N = $($Sequence.Count)"
}
(1..10).ForEach{ [string]$_ + " is " + ( Classify-AlliquotSequence -Sequence ( Get-AliquotSequence -K $_ -N 16 ) ) }
( 11, 12, 28, 496, 220, 1184, 12496, 1264460, 790, 909, 562, 1064, 1488 ).ForEach{ [string]$_ + " is " + ( Classify-AlliquotSequence -Sequence ( Get-AliquotSequence -K $_ -N 16 ) ) }

90
Task/Aliquot-sequence-classifications/PowerShell/aliquot-sequence-classifications-3.ps1 Normal file
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function Get-Aliquot
{
[CmdletBinding()]
[OutputType([PScustomObject])]
Param
(
[Parameter(Mandatory=$true,
ValueFromPipeline=$true,
ValueFromPipelineByPropertyName=$true)]
[int]
$InputObject
)
Begin
{
function Get-NextAliquot ([int]$X)
{
if ($X -gt 1)
{
$nextAliquot = 1
if ($X -gt 2)
{
$xSquareRoot = [Math]::Sqrt($X)
2..$xSquareRoot | Where-Object {$X % $_ -eq 0} | ForEach-Object {$nextAliquot += $_ + $x / $_}
if ($xSquareRoot % 1 -eq 0) {$nextAliquot -= $xSquareRoot}
}
$nextAliquot
}
}
function Get-AliquotSequence ([int]$K, [int]$N)
{
$X = $K
$X
$i = 1
while ($X -and $i -lt $N)
{
$i++
$next = Get-NextAliquot $X
if ($next)
{
if ($X -eq $next)
{
$i..$N | ForEach-Object {$X}
$i = $N
}
else
{
$X = $next
$X
}
}
else
{
$i = $N
}
}
}
function Classify-AlliquotSequence ([int[]]$Sequence)
{
$k = $Sequence[0]
if ($Sequence[-1] -eq 0) {return "terminating"}
if ($Sequence[-1] -eq 1) {return "terminating"}
if ($Sequence[1] -eq $k) {return "perfect" }
if ($Sequence[2] -eq $k) {return "amicable" }
if ($Sequence[3..($Sequence.Count-1)] -contains $k) {return "sociable" }
if ($Sequence[-1] -eq $Sequence[-2] ) {return "aspiring" }
if ($Sequence.Count -gt ($Sequence | Select -Unique).Count ) {return "cyclic" }
return "non-terminating and non-repeating through N = $($Sequence.Count)"
}
}
Process
{
$_ | ForEach-Object {
[PSCustomObject]@{
Number = $_
Classification = (Classify-AlliquotSequence -Sequence (Get-AliquotSequence -K $_ -N 16))
}
}
}
}

5
Task/Aliquot-sequence-classifications/PowerShell/aliquot-sequence-classifications-4.ps1 Normal file
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$oneToTen = 1..10 | Get-Aliquot
$selected = 11, 12, 28, 496, 220, 1184, 12496, 1264460, 790, 909, 562, 1064, 1488 | Get-Aliquot
$numbers = $oneToTen, $selected
$numbers