[seqfan] Re: Non-square composite numbers

[israel at math.ubc.ca]

Actually this is A000423.

Cheers,
Robert 

On Jul 21 2024, Robert Munafo wrote:

>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 12:34PM 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.
>
>--
>Seqfan Mailing list - http://list.seqfan.eu/
>
>