Published online by Cambridge University Press: 18 May 2009
Let s = s(a1, a2,...., ar) denote the number of integer solutions of the equation
subject to the conditions
the ai being given positive integers, and square brackets denoting the integral part. Clearly s (a1,..., ar) is also the number s = s(m) of divisors of which contain exactly λ prime factors counted according to multiplicity, and is therefore, as is proved in [1], the cardinality of the largest possible set of divisors of m, no one of which divides another.