terminology for square roots; A007913

[zak seidov]

Re: A007913  Square-free part of n: smallest number
such that n*a(n) is a square.  

1. Shouldn't we say "smallest positive number"?
Otherwise we always can take a(n)=0.

2. Also, what is a(0)?

Eric's code (see link in A007913) gives a(0)=0:

Table[Times @@ Power @@@ ({#[[1]], Mod[#[[2]], 2]}& /@
FactorInteger[n]),{n,0,11}]
(*Note: A007913 starts with  a(1)=1.
 A007913 Square-free part of n: smallest number such
that n*a(n) is a square.*)
   {0,1,2,3,1,5,6,7,2,1,10,11} 

So, there's some confusion:
a(0)=0 not 1, while a(1)=1 not 0(?!)
Zak 


--- franktaw at netscape.net wrote:

> For reference, the a's are A000188, and the d's are
> A007913.  A007913 
> calls this the square-free part; I don't know how
> standard this is.  
> A000188 doesn't really give a name, just various
> descriptions.  
> Square-free part is perhaps too easily confused with
> square-free 
> kernel, A007947, which is lcm(a,d).
> 
> Personally, I think of a as the inner square root,
> and the product a*d 
> (A019544) as the outer square root.
> 
> Integer part for a is clearly not acceptable; this
> is a synonym for the 
> floor function.  While floor is a better name than
> integer part for 
> this function, this does not make integer part
> available as a name for 
> something else.
> 
> Franklin T. Adams-Watters
> 
> 
> -----Original Message-----
> From: jrbibers at indiana.edu
> 
> Each positive integer has a square root uniquely
> expressed a product 
> a*sqrt(d), where a and d are positive integers and d
> is squarefree. 
>  
> What's the standard terminology for the parts a and
> d of some sqrt(n)? 
>  
> Some options for a: integer part, ..? 
>  
> Some options for d: quadratic part, radicand,
> squarefree part, radical 
> part, ..? 
>  
> Anyhow, the "a-part" and "d-part" of the square root
> of many 
> fundamental integer sequences are absent from EIS. 
> 
> 
>
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