k-ary Divisor

Let a Divisor $d$ of $n$ be called a 1-ary divisor if $d\perp n/d$. Then $d$ is called a $k$-ary divisor of $n$, written $d\vert _kn$, if the Greatest Common $(k-1)$-ary divisor of $d$ and $(n/d)$ is 1.

In this notation, $d\vert n$ is written $d\vert _0n$, and $d\vert\vert n$ is written $d\vert _1n$. $p^x$ is an Infinary Divisor of $p^y$ (with $y>0$) if $p^x\vert _{y-1}p^y$.

See also Divisor, Greatest Common Divisor, Infinary Divisor

References

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 54, 1994.