International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 2, Pages 343-349
Some results concerning exponential divisors
Mathematics Department, Temple University, Philadelphia 19122, PA, USA
Received 18 November 1986; Revised 9 February 1987
Copyright © 1988 Peter Hagis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
If the natural number has the canonical form then is said to be an exponential divisor of if for . The sum of the exponential divisors of is denoted by . is said to be an -perfect number if ; is said to be an -amicable pair if ; is said to be an -aliquot sequence if . Among the results established in this paper are: the density of the -perfect numbers is ; each of the first -aliquot sequences is bounded.