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Some Sum of Some Sum (Posted on 2019-10-18) Difficulty: 3 of 5
Find the sum of all the positive square-free integers whose divisors add up to 288.

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution computer solution | Comment 1 of 3
The numbers, followed by their divisors:

138
 1 23 3 69 2 46 6 138

154
 1 11 7 77 2 22 14 154

165
 1 11 5 55 3 33 15 165

213
 1 71 3 213

235
 1 47 5 235

253
 1 23 11 253


The total of 138+154+165+213+235+253 = 1158 

DefDbl A-Z
Dim crlf$, fct(20, 1), sdiv, f, dvsr, ndiv, divlist(100)


Private Sub Form_Load()
 Form1.Visible = True
 
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 For n = 2 To 288
   sdiv = 0: dvsr = 1
   ndiv = 0
   f = factor(n)
   good = 1
   For i = 1 To f
     If fct(i, 1) > 1 Then good = 0: Exit For
   Next
   If good Then
    addthem 1
    If sdiv = 288 Then
      Text1.Text = Text1.Text & n & crlf
      For i = 1 To ndiv
        Text1.Text = Text1.Text & Str(divlist(i))
      Next
      Text1.Text = Text1.Text & crlf & crlf
      tot = tot + n
    End If
   End If
   DoEvents
 Next
 
 Text1.Text = Text1.Text & crlf & tot & " done"
  
End Sub

Sub addthem(wh)
  For howmany = 0 To fct(wh, 1)
    savedvsr = dvsr
    dvsr = Int(dvsr * fct(wh, 0) ^ howmany + 0.5)
    
    If wh = f Then
      sdiv = sdiv + dvsr
      ndiv = ndiv + 1
      divlist(ndiv) = dvsr
    Else
      addthem wh + 1
    End If
    
    dvsr = savedvsr
  Next
End Sub


Function factor(num)
 diffCt = 0: good = 1
 n = Abs(num): If n > 0 Then limit = Sqr(n) Else limit = 0
 If limit <> Int(limit) Then limit = Int(limit + 1)
 dv = 2: GoSub DivideIt
 dv = 3: GoSub DivideIt
 dv = 5: GoSub DivideIt
 dv = 7
 Do Until dv > limit
   GoSub DivideIt: dv = dv + 4 '11
   GoSub DivideIt: dv = dv + 2 '13
   GoSub DivideIt: dv = dv + 4 '17
   GoSub DivideIt: dv = dv + 2 '19
   GoSub DivideIt: dv = dv + 4 '23
   GoSub DivideIt: dv = dv + 6 '29
   GoSub DivideIt: dv = dv + 2 '31
   GoSub DivideIt: dv = dv + 6 '37
   If INKEY$ = Chr$(27) Then s$ = Chr$(27): Exit Function
 Loop
 If n > 1 Then diffCt = diffCt + 1: fct(diffCt, 0) = n: fct(diffCt, 1) = 1
 factor = diffCt
 Exit Function

DivideIt:
 cnt = 0
 Do
  q = Int(n / dv)
  If q * dv = n And n > 0 Then
    n = q: cnt = cnt + 1: If n > 0 Then limit = Sqr(n) Else limit = 0
    If limit <> Int(limit) Then limit = Int(limit + 1)
   Else
    Exit Do
  End If
 Loop
 If cnt > 0 Then
   diffCt = diffCt + 1
   fct(diffCt, 0) = dv
   fct(diffCt, 1) = cnt
 End If
 Return
End Function


  Posted by Charlie on 2019-10-18 13:34:48
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