On number of ordered pair of positive integers with given least common multiple

Sajad A. Sheikh; Priyabrata Mandal

doi:10.31838/rna/2024.07.03.016

On number of ordered pair of positive integers with given least common multiple

Sajad A. Sheikh
, Priyabrata Mandal^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this article, we present an expression for the number of ordered pairs of positive integer m with a prime factorization p₁^a1 p₂^a2… p_n^an where α_i ∈ ℤ⁺ and en route introduce an identity viz: (Formula Presented) Moreover, we investigate the asymptotic behavior of the mean and variance of relative number of order pairs with some given least common multiple m. The notion of ordered pair is widely used in the fields of geometry, statistics, computing and programming languages.

Original language	English
Pages (from-to)	209-216
Number of pages	8
Journal	Results in Nonlinear Analysis
Volume	7
Issue number	3
DOIs	https://doi.org/10.31838/rna/2024.07.03.016
Publication status	Published - 22-07-2024

All Science Journal Classification (ASJC) codes

Analysis
Mathematics (miscellaneous)
Geometry and Topology
Applied Mathematics

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10.31838/rna/2024.07.03.016

Cite this

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abstract = "In this article, we present an expression for the number of ordered pairs of positive integer m with a prime factorization p1a1 p2a2… pnan where αi ∈ ℤ+ and en route introduce an identity viz: (Formula Presented) Moreover, we investigate the asymptotic behavior of the mean and variance of relative number of order pairs with some given least common multiple m. The notion of ordered pair is widely used in the fields of geometry, statistics, computing and programming languages.",

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AB - In this article, we present an expression for the number of ordered pairs of positive integer m with a prime factorization p1a1 p2a2… pnan where αi ∈ ℤ+ and en route introduce an identity viz: (Formula Presented) Moreover, we investigate the asymptotic behavior of the mean and variance of relative number of order pairs with some given least common multiple m. The notion of ordered pair is widely used in the fields of geometry, statistics, computing and programming languages.

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On number of ordered pair of positive integers with given least common multiple

Abstract

All Science Journal Classification (ASJC) codes

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