Asymptotic behavior of the irrational factor

E. Alkan, A. H. Ledoan, A. Zaharescu

Research output: Contribution to journalArticlepeer-review


We study the irrational factor function I(n) introduced by Atanassov and defined by I(n) = ∏ν=1k pν 1/αν, where n = ∏ν=1k p ν1/αν is the prime factorization of n. We show that the sequence {G(n)/n} n≧1, where G(n) = ∏ ν=1n I(ν)1/n , is convergent; this answers a question of Panaitopol. We also establish asymptotic formulas for averages of the function I(n).

Original languageEnglish (US)
Pages (from-to)293-305
Number of pages13
JournalActa Mathematica Hungarica
Issue number3
StatePublished - Nov 2008


  • Arithmetic functions
  • Averages
  • Dirichlet series
  • Irrational factor
  • Riemann zeta-function

ASJC Scopus subject areas

  • Mathematics(all)


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