[seqfan] Re: "Start a sequence at the earliest reasonable point, but no earlier."

[Charles Greathouse]

Is there any CAS that considers 1 to be non-squarefree?

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Mon, Aug 16, 2010 at 1:54 PM, zak seidov <zakseidov at yahoo.com> wrote:
>
>
> --- On Mon, 8/16/10, Donald Alan Morrison <donmorrison at gmail.com> wrote:
>
>> From: Donald Alan Morrison <donmorrison at gmail.com>
>> Subject: [seqfan] Re: "Start a sequence at the earliest reasonable point, but no earlier."
>> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
>> Cc: njas at research.att.com
>> Date: Monday, August 16, 2010, 12:37 PM
>> > It is impossible to be 100%
>> consistent!
>>
>> I agree.  My first confusion with offset numbers was
>> with the
>> squarefree numbers.  Since 1 is considered both
>> squareful and
>> squarefree, context means everything, even for
>> definitions(!)  Just
>> like the complex numbers are sometimes useful, and
>> sometimes just more
>> to think about.
>>
>> The second number (after the comma) in the offset field I
>> think should
>> be a different field though IMHO.
>>
>> sage: is_square(1)
>> True
>> sage: is_squarefree(1)
>> True
>> sage: is_square(2)
>> False
>> sage: is_squarefree(2)
>> True
>>
>
> Also,
> both PARI and Mathematica consider 1 as squarefree:
>
> PARI:
>  gp > issquare(1)
> %1 = 1
>  gp > issquarefree(1)
> %2 = 1
>
> Mathematica:
> <<NumberTheory`NumberTheoryFunctions`
> SquareFreeQ[1]
> True
>
> Zak
>
>
>
>
>
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