On the sums of complementary divisors

Mircea Becheanu*, Florian Luca, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, we study various arithmetic properties of d + n/d, where d runs through all the tau(n) positive divisors of n. For example, denoting by pi(n) the number of prime values among these sums, we study how often pi(n) > 0 and also pi(n) = tau(n), and we also evaluate the average value of pi(n). We estimate some character sums with d+ n/d and study the distribution of quadratic nonresidues and primitive roots among these sums on average over n

Original languageEnglish
Pages (from-to)635-648
Number of pages14
JournalInternational Journal of Number Theory
Issue number4
Publication statusPublished - Dec 2007


  • divisors
  • distribution of primes

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