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 $x\geq 6$.

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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
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article

A note on newly introduced arithmetic functions φ+ and σ+

Sagar Mandal
Notes on Number Theory and Discrete Mathematics
Advanced Mathematical Identities
article

A note on newly introduced arithmetic functions φ+ and σ+

Sagar Mandal
article en

Abstract

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 $x\geq 6$.

Notes on Number Theory and Discrete MathematicsVol. 31(2)
Indian Institute of Technology Kanpur (IN)
Openalex Percentile: Top 81%
Advanced Mathematical Identities
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A note on newly introduced arithmetic functions φ+ and σ+ — Sagar Mandal · Notes on Number Theory and Discrete Mathematics (2025) | TGRS Research Map | TGRS