On Enumeration of Perfect Partition

A partition of n is said to be perfect when it containe just one partition ofevery number up to n. In paper 1], Prof. Wang Efang gave some recurrenceformulas for the number of perfect n-partitions Per(n). In this paper we obtainthe explicit formula for Per(n) and discuss the condition and enumeration forperfect n-partition with the Ieast number of parts. Theorem 1. If n 1=p_1~mp_2~a…p_k~ak,p_1,p_2,…,p_k are distinc primes, a_1 a_2