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k-ary Divisor

Let a divisor d of n be called a 1-ary (or unitary) divisor if d_|_n/d (i.e., d is relatively prime to n/d). Then d is called a k-ary divisor of n, written d|_kn, if the greatest common (k-1)-ary divisor of d and (n/d) is 1 (Cohen 1990).

In this notation, d|n is written d|_0n, and d∥n is written d|_1n.

p^x is an infinitary divisor of p^y (with y>0) if p^x|_(y-1)p^y.

Suryanarayana (1968) unfortunately uses a different and conflicting definition.

See also

Biunitary Divisor, Divisor, Greatest Common Divisor, Infinitary Divisor, Unitary Divisor

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References

Abbott, P. "In and Out: k-ary Divisors." Mathematica J. 9, 702-706, 2005.Cohen, G. L. "On an Integer's Infinitary Divisors." Math. Comput. 54, 395-411, 1990.Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 54, 1994.Suryanarayana, D. "The Number of k-ary Divisors of an Integer." Monatschr. Math. 72, 445-450, 1968.

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k-ary Divisor

Cite this as:

Weisstein, Eric W. "k-ary Divisor." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/k-aryDivisor.html

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