On a Recursive Integer Sequence Implying the Nonexistence of Odd Perfect Numbers
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910982173884416 |
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| author | Dwivedi, Ritesh Yadav, Rohit |
| author_facet | Dwivedi, Ritesh Yadav, Rohit |
| contents | We define a sequence of positive integers recursively, where each term is determined as follows: starting with a given positive integer, if the term is odd, the next is the sum of its positive divisors; if the term is even, the subsequent term is half the term. In this paper, we conjecture that this sequence eventually reaches one for all initial values. Furthermore, we classify a family of integers for which this conjecture holds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01830 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a Recursive Integer Sequence Implying the Nonexistence of Odd Perfect Numbers Dwivedi, Ritesh Yadav, Rohit Number Theory 11A25, 11A51, 11Y70 We define a sequence of positive integers recursively, where each term is determined as follows: starting with a given positive integer, if the term is odd, the next is the sum of its positive divisors; if the term is even, the subsequent term is half the term. In this paper, we conjecture that this sequence eventually reaches one for all initial values. Furthermore, we classify a family of integers for which this conjecture holds. |
| title | On a Recursive Integer Sequence Implying the Nonexistence of Odd Perfect Numbers |
| topic | Number Theory 11A25, 11A51, 11Y70 |
| url | https://arxiv.org/abs/2506.01830 |