Question 618064
<pre>
There are exactly two kinds of positive integers which have 
exactly 3 proper divisors.  They are as follows:

1.  The cube of a prime p has 3 proper divisors 1, p, and pē.

2.  The product of a pair of unique primes p1, p2 has 3 proper 
divisors 1, p1, and p2.

There are 15 primes less than 50, which are

2,3,5,7,11,13,17,19,23,29,31,37,41,43,47

The number of cubes of a prime less that 50 is the number of
primes less than 50 which is also 15.

The number of products of a pair of unique primes less than 50 
is the number of pairs of primes less than 50 which is 15C2 or
{{{15*14/2}}} = 105

The total is 15 + 105 or 120.

Edwin</pre>