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The Möbius Function (and squarefree numbers)
Author

Ed Pegg
Organization: Wolfram Research, Inc.
Department: Scientific Information Group
Revision date

2003-11-01
Description

In 1831, August Ferdinand Möbius put numbers into 3 bins, as a new type of function. His procedure is represented by the Greek letter mu (µ), and is called the Möbius function in his honor.

This notebook describes some of the many fascinating properties of the MoebiusMu function, including a tool for factorization involving nontrivial zeros of the Riemann Zeta function. If there is a history for guessing MoebiusMu via this technique, please contact the author.
Subjects

*Mathematics > Calculus and Analysis > Special Functions
*Mathematics > Recreational Mathematics
Keywords

Moebius, Zeta, Mertens, factorization
URL

http://functions.wolfram.com/NumberTheoryFunctions/MoebiusMu/
http://mathworld.wolfram.com/MoebiusFunction.html
http://www.maa.org/editorial/mathgames/mathgames_11_03_03.html

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MoebiusMuFunction.nb (36.1 KB) - Mathematica Notebook