Abstract
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 language | English |
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Pages (from-to) | 635-648 |
Number of pages | 14 |
Journal | International Journal of Number Theory |
Volume | 3 |
Issue number | 4 |
DOIs | |
Publication status | Published - Dec 2007 |
Keywords
- divisors
- distribution of primes
- NUMERORUM