Partitions whose parts are pairwise relatively prime

The following problem arose in connection with our research in statistical group theory: estimate a, := the number of partitions of n into parts that are pairwise relatively prime. This differs from most problems in the theory of partitions because of the complicated relationship between the part sixes. We obtain an asymptotic formula for log a,, but leave open the challenging task of obtaining an asymptotic formula for a, itself. Let W, be the set of all partitions of n into parts that are l’s and powers of distict primes. In the language of generating functions, #FV,, is the coefficient of xn in