= Greatest common unitary divisor
A <unitary divisor> $d$ of a positive <integer> $n$ satisfies $\gcd(d,n/d)=1$. The <greatest common unitary divisor> of $a,b$ is the largest <integer> that is a <unitary divisor> of both. In their <prime factorizations>, it includes precisely those whole <prime powers> whose positive exponents agree in $a$ and $b$.
For $a=12=2^2\cdot3$ and $b=18=2\cdot3^2$, it is $1$, although the ordinary <greatest common divisor> is $6$. For $12$ and $20=2^2\cdot5$, it is $4$. Requiring unitary divisibility on both inputs is essential: merely being a <unitary divisor> of their ordinary <greatest common divisor> is a weaker condition.
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