Strong and weak Atanassov pairs

P. Spiegelhalter, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review


We study the irrational factor I(n) and the restrictive factor R(n) introduced by Atanassov and defined by I(n) = Πkv=1 p1/arv' and R(n) = Πkv=1 P vαν-1 where n = Πkv=1 pvαv is the prime factorization of n. We consider weighted combinations 7(n)o R(n)β and characterize the pairs (α,β) in order to measure how close n is to being k-power full or k-power free. We also establish an asymptotic formula for weighted averages of the function I (n)n R(n)β.

Original languageEnglish (US)
Pages (from-to)355-361
Number of pages7
JournalProceedings of the Jangjeon Mathematical Society
Issue number3
StatePublished - Jul 2011


  • Arithmetic functions
  • Irrational factor
  • Restrictive factor
  • Riemann zeta-function

ASJC Scopus subject areas

  • Mathematics(all)


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