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New page: 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...
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
{| class="wikitable"
|-
! 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
|}
[[Category:mathematics]]
*<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
{| class="wikitable"
|-
! 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
|}
[[Category:mathematics]]