On the sum of iterations of the Euler function

Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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 languageEnglish
Pages (from-to)1-5
Number of pages5
JournalJournal of Integer Sequences
Issue number1
Publication statusPublished - 23 Jan 2006


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