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

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


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.

Tags:

Notation

Elementary Number Theory

Prime Factorization

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