terminology for square roots

[franktaw at netscape.net]

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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