This paper is concerned
with the combinatorial problem of counting the number of distinct collections of
divisors of an integer N having the property that no divisor in a collection is a
multiple of any other. It is shown that if N factors into primes N = p1a1p2a2⋯pnan
the number of distinct collections of divisors with the stated property does not
exceed (∑i=1nai−n + 3)M, where M is the maximum coefficient in the expansion of
the polynomial