Möbius Mu function

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

• <math>\mu(1)=1</math>

• <math>\mu(n)=0</math> if <math>n</math> has a prime factor of power higher than 1

• <math>\mu(n)=-1</math> if <math>n</math> is prime or has an odd number of prime factors

• <math>\mu(n)=1</math> if <math>n</math> has an even number of prime factors

The first 10 values are

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