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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2509.08844 |
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| _version_ | 1866911152502472704 |
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| author | Mittou, Brahim |
| author_facet | Mittou, Brahim |
| contents | Let $d_1 = 1 < d_2 < d_3 < \cdots < d_{τ(n)} = n$ denote the increasing sequence of the divisors of a positive integer $n$. In this paper, for real or complex values of $α$, we define and study some properties of two new divisor functions $σ_{e,α}$ and $σ_{o,α}$. The first computes the sum of the $α$-th powers of the divisors of $n$ with even indices, and the second computes the sum of the $α$-th powers of the divisors of $n$ with odd indices. We also introduce a new type of positive integers, namely, $k$-index ratio numbers and state three conjectures related to them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08844 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A New Classification of Positive Integers Via New Divisor Functions Mittou, Brahim General Mathematics Let $d_1 = 1 < d_2 < d_3 < \cdots < d_{τ(n)} = n$ denote the increasing sequence of the divisors of a positive integer $n$. In this paper, for real or complex values of $α$, we define and study some properties of two new divisor functions $σ_{e,α}$ and $σ_{o,α}$. The first computes the sum of the $α$-th powers of the divisors of $n$ with even indices, and the second computes the sum of the $α$-th powers of the divisors of $n$ with odd indices. We also introduce a new type of positive integers, namely, $k$-index ratio numbers and state three conjectures related to them. |
| title | A New Classification of Positive Integers Via New Divisor Functions |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2509.08844 |