### Abstract

We study the sum F(n) =∑ k=1 κ(n) φ^{(k)}(n). of consecutive iterations of the Euler function φ(n) (where the last iteration satisfies φ^{(κ(n))}(n) = 1). We show that for almost all n, the difference |F(n) - n is not too small, and the ratio n/F(n) is not an integer. The latter result is related to a question about the so-called perfect totient numbers, for which F(n) = n.

Original language | English |
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Pages (from-to) | 1-5 |

Number of pages | 5 |

Journal | Journal of Integer Sequences |

Volume | 9 |

Issue number | 1 |

Publication status | Published - 23 Jan 2006 |

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## Cite this

Shparlinski, I. E. (2006). On the sum of iterations of the Euler function.

*Journal of Integer Sequences*,*9*(1), 1-5.