On the Composition of the Euler Function and the Dedekind Arithmetic Function
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913898910711808 |
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| author | Guo, Aimin Liu, Huan Yang, Qiyu |
| author_facet | Guo, Aimin Liu, Huan Yang, Qiyu |
| contents | Let $I(n) = \frac{ψ(ϕ(n))}{ϕ(ψ(n))}$ and $K(n) = \frac{ψ(ϕ(n))}{ϕ(ϕ(n))}$, where $ϕ(n)$ is Euler's function and $ψ(n)$ is Dedekind's arithmetic function. We obtain the maximal order of $I(n)$, as well as the average orders of $I(n)$ and $K(n)$. Additionally, we prove a density theorem for both $I(n)$ and $K(n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14633 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Composition of the Euler Function and the Dedekind Arithmetic Function Guo, Aimin Liu, Huan Yang, Qiyu Number Theory Let $I(n) = \frac{ψ(ϕ(n))}{ϕ(ψ(n))}$ and $K(n) = \frac{ψ(ϕ(n))}{ϕ(ϕ(n))}$, where $ϕ(n)$ is Euler's function and $ψ(n)$ is Dedekind's arithmetic function. We obtain the maximal order of $I(n)$, as well as the average orders of $I(n)$ and $K(n)$. Additionally, we prove a density theorem for both $I(n)$ and $K(n)$. |
| title | On the Composition of the Euler Function and the Dedekind Arithmetic Function |
| topic | Number Theory |
| url | https://arxiv.org/abs/2506.14633 |