On rough and smooth neighbors

William D. Banks; Florian Luca; Igor E. Shparlinski

On rough and smooth neighbors

William D. Banks^*, Florian Luca, Igor E. Shparlinski

^*Corresponding author for this work

School of Computing

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

Abstract

We study the behavior of the arithmetic functions defined by

F(n) = P+(n)/P-(n+1) and G(n) = P+(n + 1)/P-(n) (n >= 1),

where P+(k) and P-(k) denote the largest and the smallest prime factors, respectively, of the positive integer k.

Original language	English
Pages (from-to)	109-118
Number of pages	10
Journal	Revista Matematica Complutense
Volume	20
Issue number	1
Publication status	Published - 2007

Keywords

smallest prime divisor
largest prime divisor
PRIME FACTORS

Cite this

@article{5660a287a631449d9312a04dd1adcd25,

title = "On rough and smooth neighbors",

abstract = "We study the behavior of the arithmetic functions defined byF(n) = P+(n)/P-(n+1) and G(n) = P+(n + 1)/P-(n) (n >= 1),where P+(k) and P-(k) denote the largest and the smallest prime factors, respectively, of the positive integer k.",

keywords = "smallest prime divisor, largest prime divisor, PRIME FACTORS",

author = "Banks, {William D.} and Florian Luca and Shparlinski, {Igor E.}",

year = "2007",

language = "English",

volume = "20",

pages = "109--118",

journal = "Revista Matematica Complutense",

issn = "1139-1138",

publisher = "Springer, Springer Nature",

number = "1",

}

TY - JOUR

T1 - On rough and smooth neighbors

AU - Banks, William D.

AU - Luca, Florian

AU - Shparlinski, Igor E.

PY - 2007

Y1 - 2007

N2 - We study the behavior of the arithmetic functions defined byF(n) = P+(n)/P-(n+1) and G(n) = P+(n + 1)/P-(n) (n >= 1),where P+(k) and P-(k) denote the largest and the smallest prime factors, respectively, of the positive integer k.

AB - We study the behavior of the arithmetic functions defined byF(n) = P+(n)/P-(n+1) and G(n) = P+(n + 1)/P-(n) (n >= 1),where P+(k) and P-(k) denote the largest and the smallest prime factors, respectively, of the positive integer k.

KW - smallest prime divisor

KW - largest prime divisor

KW - PRIME FACTORS

M3 - Article

SN - 1139-1138

VL - 20

SP - 109

EP - 118

JO - Revista Matematica Complutense

JF - Revista Matematica Complutense

IS - 1

ER -

On rough and smooth neighbors

Abstract

Keywords

Fingerprint

Cite this