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Math Help - Sum of divisor function

  1. #1
    Senior Member I-Think's Avatar
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    Sum of divisor function

    I have to find a formula for the function
    f(n)=\sum_{d|n}\sigma(d)
    where
    n=p_1^{e_1}p_2^{e_2}***p_r^{e_r}

    And I want to ensure that I understand the function correctly, so I will illustrate my understanding by examples with numbers

    f(12)=\sum_{d|12}\sigma(d)
    f(12)=\sum_{d|n}24
    f(12)=60

    2nd example
    f(9)=\sum_{d|9}\sigma(d)
    f(n)=\sum_{d|n}13
    f(9)=14

    Am I correct?
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  2. #2
    MHF Contributor
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    The sum of divisors function adds up the divisors: 1 + 12 + 2 + 6 + 3 + 4 = 28
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by I-Think View Post
    I have to find a formula for the function
    f(n)=\sum_{d|n}\sigma(d)
    where
    n=p_1^{e_1}p_2^{e_2}***p_r^{e_r}

    And I want to ensure that I understand the function correctly, so I will illustrate my understanding by examples with numbers

    f(12)=\sum_{d|12}\sigma(d)
    f(12)=\sum_{d|n}24
    f(12)=60

    2nd example
    f(9)=\sum_{d|9}\sigma(d)
    f(n)=\sum_{d|n}13
    f(9)=14

    Am I correct?
    f(12)=\sigma(1)+\sigma(2)+\sigma(3)+\sigma(4)+\sig  ma(6)+\sigma(12)

    CB
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