[math-fun] Divisors of divisors

Given a multiset S, how can we determine whether there is an integer n such that each s in S corresponds to (is in bijection with) a divisor t of n such that d(t) = s? This came up recently when considering multisets with the property s_1^3 + s_2^3 + ... + s_k^3 = (s_1 + s_2 + s_3 + ... + s_k)^2. One infinite family are the multisets with this divisor-of-divisors property. Another is {n, n, ..., n} with n elements. Charles Greathouse Analyst/Programmer Case Western Reserve University