Three to the distinct-prime-factor count
= Three to the distinct-prime-factor count
{title2=$3^{\omega(n)}$}
The <multiplicative arithmetic function> $f(n)=3^{\omega(n)}$ counts assignments of three labels to each distinct <prime factor>. It also counts pairs of <squarefree divisors> whose <least common multiple> is the <radical of an integer> $n$.