Title : ( SOME RESULTS ON ORDERED AND UNORDERED FACTORIZATION OF A POSITIVE INTEGER )
Authors: Madjid Mirzavaziri , D. YAQUBI ,
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Abstract
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 positive integer n such that each factor is at least ℓ. In particular, by using elementary techniques, we give an explicit formula in the cases where k = 2, 3, 4.
Keywords
Multiplicative partition function; Set partitions; Partition function; Perfect square; Euler’s Phi function; Tau function.
@article{paperid:1103406,
author = {Madjid Mirzavaziri, and دانیال یعقوبی},
title = {SOME RESULTS ON ORDERED AND UNORDERED FACTORIZATION OF A POSITIVE INTEGER},
journal = {Journal of Algebraic Systems},
year = {2023},
volume = {12},
number = {2},
month = {January},
issn = {2345-5128},
pages = {257--267},
numpages = {10},
keywords = {Multiplicative partition function; Set partitions; Partition function; Perfect
square; Euler’s Phi function; Tau function.},
}
%0 Journal Article
%T SOME RESULTS ON ORDERED AND UNORDERED FACTORIZATION OF A POSITIVE INTEGER
%A Madjid Mirzavaziri,
%A دانیال یعقوبی
%J Journal of Algebraic Systems
%@ 2345-5128
%D 2023
