Timeline for answer to Is the least common multiple sequence $\text{lcm}(1, 2, \dots, n)$ a subset of the highly abundant numbers? by Max Alekseyev
Current License: CC BY-SA 4.0
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27 events
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| Jan 27 at 17:53 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
Code updated with safe iterator aborting per https://github.com/sagemath/sage/issues/41015
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| Oct 8, 2025 at 11:44 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
a few minor speed-up improvements to the code
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| Oct 7, 2025 at 15:48 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
Sage code bugfixed and improved
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| Oct 6, 2025 at 21:26 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
updated with thread-safe code
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| Oct 6, 2025 at 18:31 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
code updated a bit
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| Oct 6, 2025 at 15:59 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
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| Oct 6, 2025 at 15:48 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
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| Oct 6, 2025 at 15:36 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
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| Oct 6, 2025 at 15:23 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
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| Oct 6, 2025 at 15:01 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
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| Oct 6, 2025 at 14:52 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
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| Oct 5, 2025 at 17:10 | comment | added | Max Alekseyev | @TerryTao: I've added a draft sequence oeis.org/draft/A389482 (and its sister A389483) Please update as suitable. | |
| Oct 4, 2025 at 22:33 | comment | added | Terry Tao | @MaxAlekseyev I've created a separate community answer to collate these new results. | |
| Oct 4, 2025 at 22:17 | comment | added | Max Alekseyev | @TerryTao: Indeed, I also thought about such a sequence (and a sister one with no prime power restriction). I will add it after a bit more computing. | |
| Oct 4, 2025 at 22:13 | comment | added | Terry Tao | It seems like there is a non-trivial but finite OEIS sequence in the making, namely the set of $n$ which are prime powers (A000961) for which $L_n$ is highly abundant: we know the sequence has all the prime powers up to $67$, together with $81$, $83$, $89$, with the next potential element being $121$. On the other hand, the existing constructions should be able to block out large regions from this sequence; for instance, my original example blocks out $[199999, 479^2-1]=[199999,229440]$. Determining this sequence completely via crowdsourcing seems feasible. | |
| Oct 4, 2025 at 21:43 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
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| Oct 4, 2025 at 1:00 | comment | added | GH from MO | @TerryTao $L_{71}$ and $L_{73}$ are also not higly abundant... | |
| Oct 4, 2025 at 0:59 | comment | added | GH from MO | @MaxAlekseyev Yes. I updated my post accordingly. | |
| Oct 4, 2025 at 0:57 | comment | added | Max Alekseyev |
@GHfromMO: I've got same result about $L_{79}$ with the ratio M/L = 2^5 * 3 * 5 * 11 * 67^-1 * 79^-1.
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| Oct 4, 2025 at 0:54 | comment | added | Terry Tao | It's remarkable that the OEIS data was almost maximally misleading as to the truth of the OP's question. | |
| Oct 4, 2025 at 0:52 | comment | added | GH from MO | @TerryTao $L_{79}$ is also not higly abundant. I will update my post ("second response") shortly. | |
| Oct 3, 2025 at 21:52 | comment | added | Terry Tao | Nice! So only eight candidates remaining now... (and I really doubt 81 is a strong contender...) | |
| Oct 3, 2025 at 21:37 | comment | added | GH from MO | @TerryTao If I did not make a mistake, $L_{97}$ is not highly abundant. See the new section in my response. | |
| Oct 3, 2025 at 21:31 | comment | added | Terry Tao | In fact, since $L_n$ only varies at prime powers, there are only 13 remaining candidates for the minimal counterexample $n$: $67,71,73,79,81,83,89,97,101,103,107,109,113$. Anyone want to place some bets? | |
| Oct 3, 2025 at 21:07 | comment | added | Terry Tao | Nice! According to the OEIS lists provided in the comments, $L_n$ is highly abundant for $n \leq 66$, so it is now not inconceivable that with a bit more cleverness and computation (maybe involving integer programming?) one could actually find the minimal counterexample. | |
| Oct 3, 2025 at 20:00 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
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| Oct 3, 2025 at 19:44 | history | answered | Max Alekseyev | CC BY-SA 4.0 |