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Math Help - phi (201212) and phi (111111)

  1. #1
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    phi (201212) and phi (111111)

    What are the values of phi (201212) and phi (111111)?
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  2. #2
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    Re: phi (201212) and phi (111111)

    \phi(n)=n\Pi_{p|n}\left(1-\frac{1}{p}\right)

    So for example

    \phi(30)=\phi(2\times 3 \times 5)=30\times\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right) \left(1-\frac{1}{5}\right)=8.

    So factorise your numbers..

    Yes 269 is prime.
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  3. #3
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    Re: phi (201212) and phi (111111)

    I don't know how to use the symbols and I meant to say sigma function, not phi. So it would be sigma (201212) and sigma (111111)?
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  4. #4
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    Re: phi (201212) and phi (111111)

    Since sigma is a multiplicative function \sigma(mn)=\sigma(m)\sigma(n) where gcd(m,n)=1.

    So for example, \sigma(180)=\sigma(4)\sigma(9)\sigma(5)=(1+2+4) (1+3+9) (1+5)= 546
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