ON k-m-ZUMKELLER NUMBERS

In this paper we introduce the concept of k-m-Zumkeller number by partitioning the set of positive divisors of an integer n into k disjoint subsets such that the product of each subsets are equal and establish some properties on these numbers. Relations of these numbers with perfect numbers and k-m-perfect numbers are also obtained. We also define k-half-m-Zumkeller numbers and establish results on them. We also define k-T*-m-Zumkeller numbers and illustrate these numbers with suitable examples.