On the iterates of Euler's function |
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| Authors: | R Warlimont |
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| Institution: | The John Knopfmacher Centre for, Applicable Analysis and Number Theory, University of the Witwatersrand, Johannesburg 2050, South Africa, ZA
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| Abstract: | Asymptotic representations are given for the three sums ?n ￡ x j(n)/j(j(n))\textstyle\sum\limits \limits _{n\le x} \varphi (n)/\varphi \bigl (\varphi (n)\bigr ), ?n ￡ x j(n)/j(j(n))\textstyle\sum\limits \limits _{n\le x} \varphi (n)/\varphi \bigl (\varphi (n)\bigr ), ?n ￡ x log j(n)/j(j(n)) ; j\textstyle\sum\limits \limits _{n\le x}\ \log \, \varphi (n)/\varphi \bigl (\varphi (n)\bigr )\ ; \ \varphi is Euler's function. |
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