Abstract
Ghaith Hammouri
University of Hartford
The purpose of this paper is to demonstrate how the complex roots of unity can be used to
define a sequence of functions, {Gk}, that generate periodic sequences of 0’s and 1’s.
Furthermore, these functions can be summed to produce a function, S, that determines the
number of factors of an integer. The functions {Gk} are applied to denote a divisor function,
and finally the topic of Mersenne primes is discussed and some observations are made on the
factorization of the terms of sequence 2P-1.