  Let $X$ be a positive integer and $t$ a real number great than 1. The family
of sets $\left\{\big\lfloor\frac{X}{n^t}\big\rfloor ~:~ 1\leq n\leq X\right\}$
have an interesting prime distribution property. We give an exact formula for
the cardinality of these sets. We provide an estimate for the cardinality of
the set $\left\{\big\lfloor\frac{X}{p}\big\rfloor ~:~ p~ \text{prime},~ p\leq
X\right\}$. For positive real $X$, we derive asymptotic formulas for the
cardinality of the set $\big\{\lfloor f(n)\rfloor ~:~ 1\leq n\leq X\big\}$ for
various sets of functions.
