Asymptotic results for partitions (I) and the distribution of certain integers

AbstractAsymptotic results, similar to those of Roth and Szekeres, are obtained for certain partition problems. These results are then applied to the distribution of integers of the form p1d1p2d2 … prdr, where d1 ≥ d2 ≥ … ≥ dr, pi denotes the ith prime and r is arbitrary. The saddle-point method is used to obtain the asymptotic results