Between 1987 and 1989, Alladi, Erdos, and Vaaler wrote two articles that provided concrete support for the heuristic idea that "large divisors of a squarefree integer have more prime divisors than the small ones." More precisely, they investigated the ratio between the quantities sum_{d|n}(h(d)) and sum_{d|n, d<= n^{1/(t+1)}}(h(d)) when t>=1, n is a squarefree positive integer, and h:N-->R is a multiplicative arithmetic function (meaning h(lm)=h(l)h(m) whenever gcd(l,m)=1) that satisfies 0=1 is a rational number with continued fraction expansion [a_0,a_1,...,a_r], then R(h,n,t)<=1+a_0+a_1+...+a_r. In particular, R(h,n,t)<=t+1 if t is an integer. Soundararajan also showed that R(h,n,t)<=10*sqrt{omega(n)} if t is irrational. These upper bounds for R(h,n,t) beckon for improvement. First, Alladi conjectures that if t is an integer, then R(h,n,t)<=4+o(1), where o(1) tends to 0 as omega(n)-->infinity. Hence, my primary goal for this research project will be to find some absolute constant which serves as an upper bound for R(h,n,t) (possibly only when t is an integer). Even if this proves too difficult a task, it still seems possible to obtain an upper bound for R(h,n,t) that does not depend on n when t is irrational. Indeed, we know that R(h,n,t)<=t+1 when t is an integer; one should be able to produce similar bounds that do not depend on the membership of t in Z or Q.