I was able to use an extended conversation with an AI chatgpt.com/share/68ded9b1-37d… to help answer a MathOverflow question mathoverflow.net/questions/501… . I had already conducted a theoretical analysis suggesting that the answer to this question was negative, but needed some numerical parameters verifying certain inequalities in order to conclusively build a counterexample. Initially I sought to ask AI to supply Python code to search for a counterexample that I could run and adjust myself, but found that the run time was infeasible and the initial choice of parameters would have made the search doomed to failure anyway. I then switched strategies and instead engaged in a step by step conversation with the AI where it would perform heuristic calculations to locate feasible choices of parameters. Eventually, the AI was able to produce parameters which I could then verify separately (admittedly using Python code supplied by the same AI, but this was a simple 29-line program that I could visually inspect to do what was asked, and also provided numerical values in line with previous heuristic predictions).

Here, the AI tool use was a significant time saver - doing the same task unassisted would likely have required multiple hours of manual code and debugging (the AI was able to use the provided context to spot several mathematical mistakes in my requests, and fix them before generating code). Indeed I would have been very unlikely to even attempt this numerical search without AI assistance (and would have sought a theoretical asymptotic analysis instead).

Is the least common multiple sequence $\text{lcm}(1, 2, \dots, n)$ a subset of the highly abundant numbers?

I've been comparing the sequence of the Least Common Multiple of the first $n$ integers, $L_n = \text{lcm}(1, 2, \dots, n)$, with the sequence of Highly Abundant Numbers (HA). The two sequences in

^MathOverflow