Some Results on Ordered and Unordered Factorization of a Positive Integer

A well-known enumerative problem is to count the number of ways a positive integer n can be factorised as n=n₁× n₂×⋯× nₖ, where n₁ n₂ ⋯ nₖ >1. In this paper, we give some recursive formulas for the number of ordered/unordered factorizations of a positiveinteger n such that each factor is at least . In particular, by using elementary techniques, we give an explicit formula in cases where $k=2,3,4$.