  Erd\"os and Nicolas [erdos1976methodes] introduced an arithmetical function
$F(n)$ related to divisors of $n$ in short intervals $\left] \frac{t}{2},
t\right]$. The aim of this note is to prove that $F(n)$ is the largest
coefficient of polynomial $P_n(q)$ introduced by Kassel and Reutenauer
[kassel2015counting]. We deduce that $P_n(q)$ has a coefficient larger than $1$
if and only if $2n$ is the perimeter of a Pythagorean triangle. We improve a
result due to Vatne [vatne2017sequence] concerning the coefficients of
$P_n(q)$.
