[seqfan] Re: Name for a type of set needed

[Bob Selcoe]

Hi Max,

> If you look at https://oeis.org/A284311/table you notice that there's an
> error
> in the data, leading to a value of 10 instead of 64.

Thanks for catching that.  I missed 7 in the data and it threw things off.

> IMHO it would be more natural to list the numbers with given prime factors
> as rows...

Perhaps, but at this point since it's published, I don't know if it's 
appropriate to change it.  Would you suggest we still do so?

>I don't know a name for the set of numbers which has a given squarefree
> kernel (A007947), one could simply say it's the inverse image
> A007947^(-1) of that squarefree number.

I was thinking of a more generic name that possibly could be used outside of 
OEIS, something *like* "squarefree kernel sets" (though perhaps there's a 
better name) because it seems to me it's a quite useful concept that could 
be applied in many ways - including analyzing "Yellowstone" type sequences 
(e.g., A098550, A064413, A280864).  It seems like a standard name does not 
exist.

Cheers,
Bob

--------------------------------------------------
From: "M. F. Hasler" <oeis at hasler.fr>
Sent: Saturday, March 25, 2017 5:09 PM
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Name for a type of set needed

> If you look at https://oeis.org/A284311/table you notice that there's an
> error
> in the data, leading to a value of 10 instead of 64.
>
> IMHO it would be more natural to list the numbers with given prime factors
> as rows, i.e., the transposed table, s.t. the first *column* would be
> A005117 <https://oeis.org/A005117>,
> in analogy with the similar oeis.org/A182944 <https://oeis.org/A182944> .
>
> but one could simply say it's the inverse image
> A007947^(-1) of that squarefree number.
>
> Maximilian
>
> On Fri, Mar 24, 2017 at 9:24 PM, Bob Selcoe <rselcoe at entouchonline.net>
> wrote:
>
>> Hi Seqfans,
>>
>> I just proposed sequence A284311, titled: "Array T(n,k) read by
>> antidiagonals: T(1,k) = squarefree numbers > 1 in ascending order
>> (A005117(k)); columns are non-squarefree numbers (in ascending order) 
>> with
>> the exact same prime factors as T(1,k)".
>>
>> So for example, Column 6 is the set whose members have prime factors
>> {2,5}: {10, 20, 40, 50, 80, 100, 160, 200...}.
>>
>> Is there a standard name for such sets?
>>
>> Cheers,
>> Bob Selcoe
>>
>
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