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Thread: Trying to understand sigma functions

  1. #1
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    Question Trying to understand sigma functions

    Hi math forum folks!

    I'm trying to understand sigma functions in the context of a homework question that I have. I attached an image of the question in this post. The issue that I'm facing with 12c is that I got the wrong answer. To my understanding f(12) does not equal f(3) x f(4) - which is contrary to the textbook answer. I would like some clarification on why they equal each other (or if the textbook is wrong).

    Additionally, I would like to understand 12d. better. The textbook said that two sigma functions would equal another "whenever a and b have no common factors other than 1", which I don't really understand why this would be the case.

    I hope that someone can help me out!!!

    - Olivia

    Trying to understand sigma functions-screen-shot-2017-03-18-9.42.02-pm.png
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  2. #2
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    Re: Trying to understand sigma functions



    $f(12) = 1 + 2 + 3 + 4 + 6 + 12 = 28$

    $f(3) = 1 + 3 = 4$

    $f(4) = 1 + 2 + 4 = 7$

    so ... $f(3) \cdot f(4) = 28$


    I'll have to think about 12d.
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