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Summing the factors (Posted on 2018-03-08) Difficulty: 3 of 5
Let N=24* 57.

What is the sum of all N's positive factors?

Generalize.

See The Solution Submitted by Ady TZIDON    
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Solution a solution | Comment 1 of 2
The factors are all a power of 2 times a power of 5 (including zero power), so


Sigma{i=0 to 4} Sigma {j=0 to 7} (2^i * 5^j)

This comes out to 3027336. It includes 1 and the number itself.

Generalized

Sigma{i=0 to m} Sigma {j=0 to n} (a^i * b^j)

Continue adding c's, d's etc. as well as Sigmas for k, l, etc, for powers o, p, q, etc.

Or was a closed form wanted?

Does the fact that 2 and 5 were chosen imply that there may be a way of finding a closed form based on the fact that 2 and 5 are factors of the base of decimal numbers?

DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 part2 = 1
 For i = 0 To 4
 
 part5 = 1
 For j = 0 To 7
   tot = tot + part2 * part5
   part5 = part5 * 5
 Next
   part2 = part2 * 2
 Next
 Text1.Text = Text1.Text & tot & crlf
 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub


  Posted by Charlie on 2018-03-08 12:24:20
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