[seqfan] Re: Non-square composite numbers

[Allan Wechsler]

Speaking only about Maurice's primary sequence: all entries after the
second are multiples of 6. If we look at these later elements divided by 6,
we get 1, 2, 3, 4, 6, 8, 9, 12 ... which certainly looks like all the
3-smooth numbers. But then we skip 6*16 = 96, but I think this is just a
calculation error, because we certainly could have put in 96 after 72,
because 96 = 2*48 and 2 and 48 are already in the sequence.

So I conjecture that this sequence is just 2, 3, and then 6 times the
3-smooth numbers. That's not to say this *doesn't* belong in OEIS. The
definition is elegant enough that it wouldn't bother me if it got its own
entry.

On Sun, Jul 21, 2024 at 12:34 PM Maurice.Clerc--- via SeqFan <
seqfan at list.seqfan.eu> wrote:

> By studying how to pave the space with parallelepipeds I was led to
> define the following sequence:
>
> ----
> List of integers so that each one after (2,3) is the product of k=2
> different previous ones in the list. Duplicates are not allowed.
> Example:
> 2 3 6 12 18 24 36 48 54 72 108 144 162 216 288 324 432 648 864 972 1296
> 1728
>
> Note 1: they are not classical "composite numbers".
> Note 2: it could be generalized for k>2.
>
> ----
> and also ;
> - the similar one with duplicates.
> - the similar ones without any square.
>
> They don't seem to be in OEIS, but do you think it is worth adding one
> of them (or more)?
> I am not sure they are of "general interest", as required.
>
> Regards
> Maurice
>
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