Showing papers in "Publications De L'institut Mathematique in 1982"

On Sums Involving Reciprocials Of Certain Arithmetical Functions

Abstract: 1, Introduction and statement of results. Let as usual w (n) and !A (n) de note the number of distinct prime factors and the number of total prime factors of n respectively, and let P(n) denote the largest prime factor of n>2. Our aim is to estimate certain arithmetical sums (some of these estimates were posed an open problems in [4]) which will exhibit the similarities and diferences in behaviour of o(n) and O(n). Our first results are contained in the following theorems. T h e o r em 1. For x2x0 and some constants O< Cz< C, we have