  We look at extensions of formulas given by Jovovic and recently proved by
Dhar on integer partitions where the smallest part occurs at least $m$ times
and on integer partitions with fixed differences between the largest and
smallest parts where the smallest part occurs at least $k$ times. Our results
extend Dhar's results for the $m=2$ and $k=1$ cases to the general cases for
arbitrary $m$ and $k$. We also look at analogous results for overpartitions and
$\ell$-regular partitions.
