Möbius function

Möbius function
Named after	August Ferdinand Möbius
Publication year	1832
Author of publication	August Ferdinand Möbius
No. of known terms	infinite
First terms	1, −1, −1, 0, −1, 1, −1, 0, 0, 1
OEIS index	A008683; Möbius (or Moebius) function mu(n). mu(1) = 1; mu(n) = (-1)^k if n is the product of k different primes; otherwise mu(n) = 0.;

The Möbius function $\mu (n)$ is a multiplicative function in number theory introduced by the German mathematician August Ferdinand Möbius (also transliterated Moebius) in 1832. It is ubiquitous in elementary and analytic number theory and most often appears as part of its namesake the Möbius inversion formula. Following work of Gian-Carlo Rota in the 1960s, generalizations of the Möbius function were introduced into combinatorics, and are similarly denoted $\mu (x)$ .