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Recovering the number (Posted on 2019-02-13) Difficulty: 3 of 5
The sum of all divisors of this semiprime number is 2696.

What is the number?

Bonus: What if the word "semiprime" was erased from the puzzle?

No Solution Yet Submitted by Ady TZIDON    
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bonus Comment 2 of 2 |
DefDbl A-Z
Dim crlf$, fct(20, 1), sumOfDiv, f, thisFact



Private Sub Form_Load()
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 
 For n = 2 To 2696
   thisFact = 1
   sumOfDiv = 0
   f = factor(n)
   addThem 1
   If sumOfDiv = 2696 Then
      Text1.Text = Text1.Text & n & Str(sumOfDiv) & crlf
   End If
 Next
 
 
 
 Text1.Text = Text1.Text & Str(tot2)
End Sub

Sub addThem(wh)
  pwr = 1
  For p = 0 To fct(wh, 1)
    thisFact = thisFact * pwr
    If wh = f Then
     sumOfDiv = sumOfDiv + thisFact
    Else
     addThem wh + 1
    End If
    thisFact = thisFact / pwr
    pwr = pwr * fct(wh, 0)
  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

finds only the semiprime solution, so erasing "semiprime" from the puzzle doesn't add any solutions.

  Posted by Charlie on 2019-02-13 13:43:15
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