[seqfan] Re: Non-square composite numbers

[Robert Munafo]

Hi Maurice,

Replicating your definition I get 2*48=96 as a term, and that leads to
additional terms that your version "misses".

2, 3, 6, 12, 18, 24, 36, 48, 54, 72, 96, 108, 144, 162, 192, 216, 288,
324, 384, 432, 486, 576, 648, 768, 864, 972, 1152, 1296, 1458, 1536,
1728, ...

Ignoring the initial 2,3 this sequence is A187778.

100 terms from my program:

Clerc01[] = 2, 3, 6, 12, 18, 24, 36, 48, 54, 72, 96, 108, 144, 162,
192, 216, 288, 324, 384, 432, 486, 576, 648, 768, 864, 972, 1152,
1296, 1458, 1536, 1728, 1944, 2304, 2592, 2916, 3072, 3456, 3888,
4374, 4608, 5184, 5832, 6144, 6912, 7776, 8748, 9216, 10368, 11664,
12288, 13122, 13824, 15552, 17496, 18432, 20736, 23328, 24576, 26244,
27648, 31104, 34992, 36864, 39366, 41472, 46656, 49152, 52488, 55296,
62208, 69984, 73728, 78732, 82944, 93312, 98304, 104976, 110592,
118098, 124416, 139968, 147456, 157464, 165888, 186624, 196608,
209952, 221184, 236196, 248832, 279936, 294912, 314928, 331776,
354294, 373248, 393216, 419904, 442368, ...

--
  Robert Munafo, mrob27 at gmail.com

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.