Dense Number Sequence
Jelly, 9 bytes
ÆE²Sḍ2µ#Ṫ
Reads from STDIN and uses 1-based indexing. Try it online!
How it works
ÆE²Sḍ2µ#Ṫ Main link. No arguments. Implicit argument: 0
µ# Read an integer n from STDIN and execute the chain to the left for
k = 0, 1, 2, ... until n of them return a truthy value.
Return the array of matches.
ÆE Compute the exponents of k's prime factorization.
² Square each exponent.
S Compute the sum of all squares.
ḍ2 Test if 2 is divisible by the result (true iff the sum is 1 or 2).
Ṫ Tail; extract the last (n-th) matching value of k.