When factorization of integer $x$ is $x=p_{1}^{e_1} p_{2}^{e_{2}} \cdots p_{n}^{e_n}$, I'd like to notate the sum of exponents; $f(x)=e_{1}+e_2 + \cdots +e_{n}$. Is it already defined or named?
2026-03-28 22:37:11.1774737431
sum of exponents
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OEIS A001222 denotes this as $\Omega(x)$ "Omega: Number of prime divisors counted with multiplicity":
$$\Omega\big(\prod_i p_i^{e_i}\big) := \sum_i e_i$$
FYI, A001221 denotes the sum of exponents without multiplicity as $\omega(x)$ "omega".