[seqfan] Re: Potentially dumb question: Is 1 squarefree?
jfb at brennen.net
Sat Feb 12 02:44:49 CET 2011
To preserve fundamental ideas about squarefree numbers, I
think that 1 must be considered squarefree. In particular,
the idea that given two positive integers A and B, their
product AB is squarefree if and only if A is squarefree,
B is squarefree, and gcd(A,B)==1. (Note that this implies
the reverse assertion that every divisor of a squarefree
number is also squarefree.)
Disallow 1 as a squarefree number and your fundamental
ideas now require exceptions, and get a whole lot messier.
On 2/11/2011 3:50 PM, Alonso Del Arte wrote:
> Is 1 a squarefree number?
> On the one hand, mu(1) = 1.
> On the other hand, sqrt(1) is an integer, just like 4, 9, 16, 25, ...
> (though unlike 12, 18, 80, ...)
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