A note on newly introduced arithmetic functions φ+ and σ+
In a recent paper [7], the authors introduced new arithmetic functions $\varphi^+$, $\sigma^+$ related to the classical functions $\varphi$, and $\sigma$, respectively. In this note, we study the behavior of $$\sum_{\substack{n\leq x\\ \omega(n)=2}}(\varphi^{+}-\varphi)(n),~~~\text{and}~~\sum_{\substack{n\leq x\\ \omega(n)=2}}(\sigma^{+}-\sigma)(n),$$ for any real number $x\geq 6$.
Authors
- Sagar Mandal (ORCID: https://orcid.org/0000-0001-8256-4384)
Institutions
- Indian Institute of Technology Kanpur (IN)
Publication Details
- Journal
- Notes on Number Theory and Discrete Mathematics
- Published
- 2025-01-01
- DOI
- https://doi.org/10.7546/nntdm.2025.31.2.404-409
- Primary Topic
- Advanced Mathematical Identities
- Type
- article
- Field-Weighted Citation Impact
- 0.00