Möbius Mu function

The Möbius mu function denoted $\mu (n)$ supported on the natural numbers and has implications in number theory. It has the value,

• $\mu (1)=1$

• $\mu (n)=0$ if Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} has a prime factor of power higher than 1

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu(n)=-1} if $n$ is prime or has an odd number of prime factors

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu(n)=1} if Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} has an even number of prime factors

The first 10 values are

n	factors	$\mu (n)$
1	n/a	1
2	2	-1
3	3	-1
4	$2^{2}$	0
5	5	-1
6	2,3	1
7	7	-1
8	$2^{3}$	0
9	$3^{2}$	0
10	2,5	1