Divisors mu Möbius

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

g(n)=∑d|nf(d)

for every integer n≥1, then

f(n)=∑d|nμ(d)g(nd)

for every integer n≥1, 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=n∑d|nμ(d)≠01μ(d)·d

Syntax

divisors_mu_moebius(Integer)

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

Syntax Description