On the values of the divisor function

Florian Luca*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


For a positive integer n we let τ(n) denote the number of its positive divisors. In this paper, we obtain lower and upper bounds for the average value of the ratio τ(n + 1)/τ(n) as n ranges through positive integers in the interval [1,x]. We also study the cardinality of the sets {τ(p - 1) : p ≤ x prime} and {τ(2n - 1) : n ≤ x}.

Original languageEnglish
Pages (from-to)59-69
Number of pages11
JournalMonatshefte fur Mathematik
Issue number1
Publication statusPublished - May 2008


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