The number of odd proper divisors of$3^p{.6}^m{.21}^n$ is

$3^p{.6}^m{.21}^n=2^m{.3}^{p+m+n}{.7}^n$

$\therefore$ The required number of proper divisors

 = Number of selection of any number of 3’s and 7’s

[$\therefore$ for odd divisors 2 must not be selected]

$=\left(p+m+n+1\right)\left(n+1\right)-1$ .