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On some sums involving the integral part function.
- Source :
-
International Journal of Number Theory . Apr2024, Vol. 20 Issue 3, p831-847. 17p. - Publication Year :
- 2024
-
Abstract
- Denote by τ k (n) , ω (n) and μ 2 (n) the number of representations of n as a product of k natural numbers, the number of distinct prime factors of n and the characteristic function of the square-free integers, respectively. Let [ t ] be the integral part of real number t. For f = ω , 2 ω , μ 2 , τ k , we prove that ∑ n ≤ x f x n = x ∑ d ≥ 1 f (d) d (d + 1) + O (x f + ) for x → ∞ , where ω = 5 3 1 1 0 , 2 ω = 9 1 9 , μ 2 = 2 5 , τ k = 5 k − 1 1 0 k − 1 and > 0 is an arbitrarily small positive number. These improve the corresponding results of Bordellès. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 17930421
- Volume :
- 20
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- International Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 176852208
- Full Text :
- https://doi.org/10.1142/S179304212450043X