64 lines
1.9 KiB
Plaintext
64 lines
1.9 KiB
Plaintext
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 ) ) }
|