Mertens Accumulation of Möbius Values

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

The Möbius function is defined for positive integers by , for distinct primes , and 0 otherwise. The Mertens function is the cumulative sum of the Möbius function.


The left graphic shows the first values of the Möbius function, reading right-to-left and top-to-bottom, and coded by color using red for -1, green for 0, and blue for 1. The right graphic shows the corresponding values of the Mertens function; values that are not -1, 0, or 1 are shown in levels of gray.


Contributed by: Michael Schreiber (March 2011)
Open content licensed under CC BY-NC-SA



Gauss studied the Möbius function before Möbius.

MoebiusMu is the built-in implementation of the Möbius function in Mathematica. The Möbius function returns 1 for 1 by definition.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.