In other words, the sphenic numbers are the square-free 3-almost primes.
, where p, q, and r are distinct primes, then the set of divisors of n will be: The converse does not hold.
All sphenic numbers are by definition squarefree, because the prime factors must be distinct.
This is easily provable by the multiplication process at a minimum adding another prime factor, or raising an existing factor to a higher power.
There is no case of more than three, because every fourth consecutive positive integer is divisible by 4 = 2×2 and therefore not squarefree.