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SquareFreeQ vs. MoebiusMu

• To: mathgroup at smc.vnet.net
• Subject: [mg30144] SquareFreeQ vs. MoebiusMu
• From: "Harvey P. Dale" <hpd1 at nyu.edu>
• Date: Tue, 31 Jul 2001 04:27:17 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

The function SquareFreeQ[n], in NumberTheory`NumberTheoryFunctions`, appears
to do the same thing as testing for MoebiusMu[n] being unequal to zero.  The
latter, however, is several thousand times as fast.  Is there ever any
reason for using SquareFreeQ?  If not, why is it included in the standard
Add-On package?
	I should add that at page 317 of the Mathematica 4 Standard Add-On
Packages volume, SquareFreeQ is erroneously described.  It says the
function will give True if n contains a squared factor, False otherwise.
That is exactly backwards.
	Best,
	Harvey


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