k-ary Divisor
المؤلف:
Guy, R. K.
المصدر:
nsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag
الجزء والصفحة:
...
25-11-2020
772
k-ary Divisor
Let a divisor 
of 
be called a 1-ary (or unitary) divisor if 
(i.e., 
is relatively prime to 
). Then 
is called a 
-ary divisor of 
, written 
, if the greatest common 
-ary divisor of 
and 
is 1 (Cohen 1990).
In this notation, 
is written 
, and 
is written 
.
is an infinitary divisor of 
(with 
) if 
.
Suryanarayana (1968) unfortunately uses a different and conflicting definition.
REFERENCES:
Abbott, P. "In and Out: 
-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 
-ary Divisors of an Integer." Monatschr. Math. 72, 445-450, 1968.
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