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Divisors mu Möbius

Möbius inversion formula states that if g and f are arithmetic functions satisfying

g(n)=d|nf(d)

for every integer n1, then

f(n)=d|nμ(d)g(nd)

for every integer n1, where μ(d) is the Möbius function. Phi Euler's function satisfies

n=d|nφ(d)

Then, applying Möbius inversion formula we can write

φ(n)=d|nμ(d)nd=nd|nμ(d)01μ(d)·d

Syntax

divisors_mu_moebius(Integer)

Description

Given an integer n, returns a list with the divisors of nn multiplied by μ(d)\mu(d).

arithmetic.divisors_mu_moebius.calc.png