A question about the omega functions \Omega (n) and \omega (n)

Given a random positive number $n$ , is there a way to determine the number of prime factors of $n$ without factorizing $n$ ?

There are several useful primality tests for a given number, such as the Miller-Rabin primality test, but is there a test to determine whether number is a semiprime or a 3-almost prime, etc.? Put another way, how can one find either the total number of prime factors (counted with multiplicity) or the number of distinct prime factors without factoring $n$ ?

After some digging in Wikipedia, I found that these two properties, the number of prime factors to muliplicity and number of distinct prime factors, could be described, respectively, by the functions $\Omega (n)$ and $\omega (n)$ .

Thus, we have another way to phrase the question: "Is there a way to calculate either of the omega functions for $n$ without knowing any of the factors of $n$ ?"

There wasn't much information on those functions at Wikipedia though, and I couldn't parse the information in the notes for the related OEIS sequences.

Here are some links that may be relevant: Prime factor; Prime power decomposition; A001222, The number of prime factors counted with multiplicity, $\Omega (n)$ ; A001221, The number of distinct primes dividing n, $\omega (n)$

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Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

A question about the omega functions Ω(n) \Omega (n) Ω(n) and ω(n) \omega (n) ω(n)

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A question about the omega functions $\Omega (n)$ and $\omega (n)$