Is there a name/notation for the sum of the powers in a prime factorization

Question

Let $n=p_1^{\alpha_1}p_2^{\alpha_2}\cdots p_k^{\alpha_k}$, where $p_i$'s are distinct primes and $\alpha_i \geq 1$ for all $i$.

Is there any name & notation for the number $\alpha_1 + \alpha_2+ \cdots + \alpha_k$?

Answer 1

It is $\Omega(n)$, that is number of prime divisors of $n$ counted with multiplicity.

See the OEIS sequence A001222 for references. I would like to mention the paper:

Robert E. Dressler and Jan van de Lune, "Some remarks concerning the number theoretic functions $\omega(n)$ and $\Omega(n)$", Proc. Amer. Math. Soc. 41 (1973), 403-406

Answer 2

Usually $\omega(n)$ denotes the number of distinct prime factors of n, and $\Omega(n)$ denotes the number of prime factors counting multiplicity, which is exactly what you are looking for.

Answer 3

The expression $\alpha_{1} + \dots + \alpha_{n}$ is the sum of the p-adic orders of the prime factors. Take a closer look here