WikiLean Articles · Brain · Recent changes · Proposals · Flags · Stats · About

Diff — Möbius function

Revision #1407 → #2731 · back to history

modifiedDefinition of the Möbius function9ffbbbda7215
FieldFrom #1407To #2731
anchors[{"section":"Definition","snippet":"The Möbius function is defined by"},{"type":"math_alttext","value":"{\\displaystyle \\mu (n)={\\begin{cases}1&{\\text{if }}n=1\\\\(-1)^{k}&{\\text{if }}n{\\text{ is the product of }}k{\\text{ distinct primes}}\\\\0&{\\text{if }}n{\\text{ is divisible by a square}}>1.\\end{cases}}}"}]
addedMöbius inversion formulac4dcbbf8ff95
addedSum-over-divisors as Dirichlet convolution μ*ζ = 19406476e1d54
modifiedIterated Dirichlet convolution of the Möbius function6227ac9b7ef9
FieldFrom #1407To #2731
anchors[{"section":"Incidence algebras","snippet":"so is its (iterated) Dirichlet convolution"},{"type":"math_alttext","value":"{\\displaystyle \\mu _{k}\\left(p^{a}\\right)=(-1)^{a}{\\binom {k}{a}}}"}]