Abstract
In this paper, we study various arithmetic properties of d + n/d, where d runs through all the τ(n) positive divisors of n. For example, denoting by ϖ(n) the number of prime values among these sums, we study how often ϖ(n) > 0 and also ϖ(n) = τ(n), and we also evaluate the average value of ϖ(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 ≤ x.
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