SOME RESULTS ON ORDERED AND UNORDERED FACTORIZATION OF A POSITIVE INTEGER

Author(s):

Daniel Yaqubi * , Madjid Mirzavaziri

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

A well-known enumerative problem is to count the number of ways a positive integer $n$ can be factorised as $n=n_1\times n_2\times\cdots\times n_{k}$, where $n_1\geqslant n_2 \geqslant \cdots \geqslant n_{k} >1$. 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 $\ell$. In particular, by using elementary techniques, we give an explicit formula in cases where $k=2,3,4$.

Keywords:

Multiplicative partition function , Set partitions , Partition function , Perfect square , Euler's Phi function

Language:
English
Published:
Journal of Algebraic Systems, Volume:12 Issue: 2, Winter-Spring 2025
Pages:
257 to 267
https://www.magiran.com/p2637384