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 Summing the factors (Posted on 2018-03-08)
Let N=24* 57.

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

Generalize.

 See The Solution Submitted by Ady TZIDON No Rating

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 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\$

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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