New posts in mobius-function

Prove that $\mu(n)\mu(n+1)\mu(n+2)\mu(n+3)=0$ for $n\ge 1$

number-theory elementary-number-theory mobius-function

What is the Möbius analoge for Ihara's $\zeta$ function?

graph-theory riemann-zeta zeta-functions mobius-function

Are there infinitely many natural numbers $n$ such that $\mu(n)=\mu(n+1)=\pm 1$?

number-theory mobius-function

The meaning and definition of $\psi^{(-2)}(x)$, and the convergence of some related series involving the Möbius function

derivatives convergence-divergence mobius-function polygamma digamma-function

A problem involving the product $\prod_{k=1}^{n} k^{\mu(k)}$, where $\mu$ denotes the Möbius function

sequences-and-series number-theory mobius-function

Prove sum of primitive roots congruent to $\mu(p-1) \pmod{p}$

number-theory primitive-roots mobius-function

The Möbius function is the sum of the primitive $n$th roots of unity. [duplicate]

number-theory analytic-number-theory mobius-function

Is there a "nice" formula for $\sum_{d|n}\mu(d)\phi(d)$?

elementary-number-theory arithmetic-functions mobius-function dirichlet-convolution

Coefficient of $n$th cyclotomic polynomial equals $-\mu(n)$

abstract-algebra number-theory polynomials cyclotomic-polynomials mobius-function

Divisor sum property of Euler phi function with Mobius inversion

number-theory elementary-number-theory analytic-number-theory totient-function mobius-function

Prove $\sum_{d \leq x} \mu(d)\left\lfloor \frac xd \right\rfloor = 1 $

number-theory arithmetic-functions mobius-function

what is the mobius transformation that maps a circle with center $z_0$ and radius $R$ to the unit circle?

complex-analysis geometry mobius-transformation mobius-function