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Erdős’s Work on the Sum of Divisors Function and on Euler’s Function

  • Andrzej Schinzel
Part of the Bolyai Society Mathematical Studies book series (BSMS, volume 25)

Abstract

The following notation will be used throughout log r x is the r times iterated logarithm of x,
$$\begin{gathered}\sigma _1 (n) = \sigma (n),\quad \sigma _k (n) = \sigma (\sigma _{k - 1} (n)), \hfill \\\phi _1 (n) = \phi (n),\quad \phi _k (n) = \phi (\phi _{k - 1} (n)), \hfill \\s_1 (n) = s(n) = \quad \sigma (n) - n,\quad s_i (n) = s_1 (s_{i - 1} (n)); \hfill \\\end{gathered}$$
ψ is Euler’s constant, \(\alpha _0 = \log \Pi _p \;prime\;(1 - \frac{1}{p})^{ - 1/p}\). Density is always the asymptotic density.

Keywords

Positive Integer Number Theory Arithmetic Function Acta Arith Analytic Number Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag 2013

Authors and Affiliations

  • Andrzej Schinzel
    • 1
  1. 1.Institute of MathematicsPolish Academy of SciencesWarsawPoland

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