MathDB

A finite set

S

of positive integers has the property that, for each

s \in S,

and each positive integer divisor

d

s

, there exists a unique element

t \in S

satisfying

\text{gcd}(s, t) = d

. (The elements

s

and

t

could be equal.)
Given this information, find all possible values for the number of elements of

S

5