' Function to get divisors of a number
Sub getDivisors(n As Integer, divs() As Integer)
    Redim divs(1)
    divs(0) = 1
    divs(1) = n
    Dim As Integer i = 2, j
    While i * i <= n
        If n Mod i = 0 Then
            j = n \ i
            Redim Preserve divs(Ubound(divs) + 1)
            divs(Ubound(divs)) = i
            If i <> j Then
                Redim Preserve divs(Ubound(divs) + 1)
                divs(Ubound(divs)) = j
            End If
        End If
        i += 1
    Wend
End Sub

' Function to check if a sum can be formed by a subset of divisors
Function isPartSum(divs() As Integer, sum As Integer) As Boolean
    If sum = 0 Then Return True

    Dim le As Integer = Ubound(divs) + 1
    If le = 0 Then Return False

    Dim last As Integer = divs(le - 1)
    Dim newDivs(le - 2) As Integer
    For i As Integer = 0 To le - 2
        newDivs(i) = divs(i)
    Next
    If last > sum Then Return isPartSum(newDivs(), sum)

    Return isPartSum(newDivs(), sum) Orelse isPartSum(newDivs(), sum - last)
End Function

' Function to check if a number is a Zumkeller number
Function isZumkeller(n As Integer) As Boolean
    Dim divs() As Integer
    getDivisors(n, divs())
    Dim sum As Integer = 0
    For i As Integer = 0 To Ubound(divs)
        sum += divs(i)
    Next
    ' if sum is odd can't be split into two partitions with equal sums
    If sum Mod 2 = 1 Then Return False
    ' if n is odd use 'abundant odd number' optimization
    If n Mod 2 = 1 Then
        Dim abundance As Integer = sum - 2 * n
        Return abundance > 0 Andalso abundance Mod 2 = 0
    End If
    ' if n and sum are both even check if there's a partition which totals sum / 2
    Return isPartSum(divs(), sum \ 2)
End Function

Sub main()
    Print "The first 220 Zumkeller numbers are:"
    Dim As Integer i = 2
    Dim As Integer cnt = 0
    While cnt < 220
        If isZumkeller(i) Then
            Print Using "### "; i;
            cnt += 1
            If cnt Mod 20 = 0 Then Print
        End If
        i += 1
    Wend

    Print !"\nThe first 40 odd Zumkeller numbers are:"
    i = 3
    cnt = 0
    While cnt < 40
        If isZumkeller(i) Then
            Print Using "##### "; i;
            cnt += 1
            If cnt Mod 10 = 0 Then Print
        End If
        i += 2
    Wend

    Print !"\nThe first 40 odd Zumkeller numbers which don't end in 5 are:"
    i = 3
    cnt = 0
    While cnt < 40
        If i Mod 10 <> 5 Andalso isZumkeller(i) Then
            Print Using "####### "; i;
            cnt += 1
            If cnt Mod 8 = 0 Then Print
        End If
        i += 2
    Wend
End Sub

main()
Sleep