September 2017 Update

Task/Aliquot-sequence-classifications/PowerShell/aliquot-sequence-classifications-3.psh

@@ -0,0 +1,90 @@
+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))
+            }
+        }
+    }
+}

Task/Aliquot-sequence-classifications/PowerShell/aliquot-sequence-classifications-4.psh

@@ -0,0 +1,5 @@
+$oneToTen = 1..10 | Get-Aliquot
+$selected = 11, 12, 28, 496, 220, 1184, 12496, 1264460, 790, 909, 562, 1064, 1488 | Get-Aliquot
+
+$numbers = $oneToTen, $selected
+$numbers