Y by Adventure10
For a positive integer
, let
if
is not squarefree and
if
is a product of
primes, and let
be the sum of the divisors of
. Prove that for all
we have
![\[\left|\sum_{d|n}\frac{\mu(d)\sigma(d)}{d}\right| \geq \frac{1}{n}, \]](//latex.artofproblemsolving.com/8/e/b/8eb88de7cd7ea8e2853dbc80cae24bdc6b77f9be.png)
and determine when equality holds.
Wenyu Cao.









![\[\left|\sum_{d|n}\frac{\mu(d)\sigma(d)}{d}\right| \geq \frac{1}{n}, \]](http://latex.artofproblemsolving.com/8/e/b/8eb88de7cd7ea8e2853dbc80cae24bdc6b77f9be.png)
and determine when equality holds.
Wenyu Cao.