Explicit formulas for Euler's totient function and the number of divisors
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913834532339712 |
|---|---|
| author | Pain, Jean-Christophe |
| author_facet | Pain, Jean-Christophe |
| contents | In this article, we present relations for the Euler totient function $φ(n)$ and the number of divisors $τ(n)$ in terms of finite sums of integer parts of rational numbers or greatest common divisors of pairs of integers. Some of the formulas are obtained using a relation due to Menon and the connections with the Pillai arithmetic function are outlined. The reported expressions may be useful to derive new bounds for the usual arithmetical functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08434 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit formulas for Euler's totient function and the number of divisors Pain, Jean-Christophe Number Theory In this article, we present relations for the Euler totient function $φ(n)$ and the number of divisors $τ(n)$ in terms of finite sums of integer parts of rational numbers or greatest common divisors of pairs of integers. Some of the formulas are obtained using a relation due to Menon and the connections with the Pillai arithmetic function are outlined. The reported expressions may be useful to derive new bounds for the usual arithmetical functions. |
| title | Explicit formulas for Euler's totient function and the number of divisors |
| topic | Number Theory |
| url | https://arxiv.org/abs/2505.08434 |