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OEIS: [A167171](https://oeis.org/A167171)

A *dense number* is a number that has exactly as many prime divisors as non-prime divisors (including 1 and itself as divisors). Equivalently, it is either a prime or a product of two distinct primes. The first 100 dense numbers are:

2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 67, 69, 71, 73, 74, 77, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 103, 106, 107, 109, 111, 113, 115, 118, 119, 122, 123, 127, 129, 131, 133, 134, 137, 139, 141, 142, 143, 145, 146, 149, 151, 155, 157, 158, 159, 161, 163, 166, 167, 173, 177, 178, 179, 181, 183, 185, 187, 191, 193, 194

Given a nonnegative integer `n`, output `dense(n)`. `n` may be 0-indexed or 1-indexed.

## Reference implementation (Sage)

import itertools
 
 def dense_numbers():
 n = 1
 while True:
 prime_divisors = [x for x in divisors(n) if x.is_prime()]
 non_prime_divisors = [x for x in divisors(n) if not x.is_prime()]
 if len(prime_divisors) == len(non_prime_divisors):
 yield n
 n += 1
 
 N = 20
 
 print itertools.islice(dense_numbers(), N, N+1).next()

[Try it online](http://sagecell.sagemath.org/?z=eJyVkMEKwjAMhu-FvkOOLZPhPAp7hZ28iQy0GQa6dLSdzre3m8qm4sGfHkr-9sufUNs5H4Ei-uicDVJIYbABgxyw5r49og9Kb6WAJIYSisf1eiaLsPM9Pr1RnacWa0MXCs6H9Hg_QOM8DEAMr7JiDdTAkFOopw9KH2YEO67_wbCLv1DJtcjqnaahLKfydyO9mGTUjdAa4EU2yKb5pahSqM16dqRIKF7sMSWydEL1sccVVOlkhc4Zh6j0HWNmcbU=&lang=sage)

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