Infinary Divisor

$p^x$ is an infinary divisor of $p^y$ (with $y>0$) if $p^x\vert _{y-1}p^y$. This generalizes the concept of the k-ary Divisor.

See also Infinary Perfect Number, k-ary Divisor

References

Cohen, G. L. ``On an Integer's Infinary Divisors.'' Math. Comput. 54, 395-411, 1990.

Cohen, G. and Hagis, P. ``Arithmetic Functions Associated with the Infinary Divisors of an Integer.'' Internat. J. Math. Math. Sci. 16, 373-383, 1993.

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