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Erdős Problem #1061

Number theory · candidate

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Statement

For S(x)=#{(a,b):a+b≤x, σ(a)+σ(b)=σ(a+b)}S(x) = \#\{(a,b) : a + b \le x,\ \sigma(a) + \sigma(b) = \sigma(a+b)\}, is S(x)∼cxS(x) \sim cx? The preprint claims S(x)S(x) grows faster than x(log⁡x)Rx (\log x)^R for every fixed RR, ruling out the linear asymptotic.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    ChatGPT

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

    VibeMathed records no account of how ChatGPT was used here. See erdosproblems.com/1061.

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