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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2501.10616 |
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| _version_ | 1866909460576862208 |
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| author | Vela, Luis Palacios Wolird, Christian |
| author_facet | Vela, Luis Palacios Wolird, Christian |
| contents | We give a closed-form expression for $φ(1+φ(2+φ(3+...+φ(n)$, where $φ$ is Euler's totient function. More generally, for an integer sequence $A=\{a_j\}$ we study the value of $A^φ(n)=φ(a_1+φ(a_2+φ(a_3+...+φ(a_n)$ when $A$ is the perfect squares or the perfect cubes. We show $A^φ(n)$ is bounded for all sequences considered. We also present the Arboreal Algorithm which can sometimes determine a closed form of $A^φ(n)$ using tree-like structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10616 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Forestry of Adversarial Totient Iterations Vela, Luis Palacios Wolird, Christian Number Theory Dynamical Systems We give a closed-form expression for $φ(1+φ(2+φ(3+...+φ(n)$, where $φ$ is Euler's totient function. More generally, for an integer sequence $A=\{a_j\}$ we study the value of $A^φ(n)=φ(a_1+φ(a_2+φ(a_3+...+φ(a_n)$ when $A$ is the perfect squares or the perfect cubes. We show $A^φ(n)$ is bounded for all sequences considered. We also present the Arboreal Algorithm which can sometimes determine a closed form of $A^φ(n)$ using tree-like structures. |
| title | The Forestry of Adversarial Totient Iterations |
| topic | Number Theory Dynamical Systems |
| url | https://arxiv.org/abs/2501.10616 |