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arXiv · 2506.01830

On a Recursive Integer Sequence Implying the Nonexistence of Odd Perfect Numbers

Ritesh Dwivedi·Rohit Yadav
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Abstract

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.

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Ritesh Dwivedi, Rohit Yadav. 2025-06-02. On a Recursive Integer Sequence Implying the Nonexistence of Odd Perfect Numbers. https://arxiv.org/abs/2506.01830

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