On the Within-perfect Numbers
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916386531442688 |
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| author | Kwan, Chung-Hang Miller, Steven J. |
| author_facet | Kwan, Chung-Hang Miller, Steven J. |
| contents | Motivated by the works of Erdös, Pomerance, Wolke and Harman on the sum-of-divisor function $σ(n)$, we study the distribution of a special class of natural numbers closely related to (multiply) perfect numbers which we term `$(\ell;k)$-within-perfect numbers', where $\ell >1$ is a real number and $k: [1, \infty) \rightarrow (0, \infty)$ is an increasing and unbounded function. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_06892 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Within-perfect Numbers Kwan, Chung-Hang Miller, Steven J. Number Theory 11A25 (primary), 11N25, 11B83 (secondary) Motivated by the works of Erdös, Pomerance, Wolke and Harman on the sum-of-divisor function $σ(n)$, we study the distribution of a special class of natural numbers closely related to (multiply) perfect numbers which we term `$(\ell;k)$-within-perfect numbers', where $\ell >1$ is a real number and $k: [1, \infty) \rightarrow (0, \infty)$ is an increasing and unbounded function. |
| title | On the Within-perfect Numbers |
| topic | Number Theory 11A25 (primary), 11N25, 11B83 (secondary) |
| url | https://arxiv.org/abs/2406.06892 |