This site is supported by donations to The OEIS Foundation.

In number theory, completely additive arithmetic functions are arithmetic functions ${\displaystyle \scriptstyle a(n),\,n\,\in \,\mathbb {N} ^{+},\,}$ such that
${\displaystyle a(mn)=a(m)+a(n),\quad m,\,n\in \mathbb {N} ^{+}.\,}$
Obviously, ${\displaystyle \scriptstyle a(1)}$ must be 0. An example is ${\displaystyle \Omega (n)}$, the number of prime factors of ${\displaystyle n}$.