On the distribution of $ϕ(σ(n))$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913458122915840 |
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| author | Bhattacharjee, Saunak Dixit, Anup B. |
| author_facet | Bhattacharjee, Saunak Dixit, Anup B. |
| contents | Let $ϕ(n)$ be the Euler totient function and $σ(n)$ denote the sum of divisors of $n$. In this note, we obtain explicit upper bounds on the number of positive integers $n\leq x$ such that $ϕ(σ(n)) > cn$ for any $c>0$. This is a refinement of a result of Alaoglu and Erdős. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01936 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the distribution of $ϕ(σ(n))$ Bhattacharjee, Saunak Dixit, Anup B. Number Theory 11N37, 11N36, 11N64 Let $ϕ(n)$ be the Euler totient function and $σ(n)$ denote the sum of divisors of $n$. In this note, we obtain explicit upper bounds on the number of positive integers $n\leq x$ such that $ϕ(σ(n)) > cn$ for any $c>0$. This is a refinement of a result of Alaoglu and Erdős. |
| title | On the distribution of $ϕ(σ(n))$ |
| topic | Number Theory 11N37, 11N36, 11N64 |
| url | https://arxiv.org/abs/2408.01936 |