Sums of Numbers with Many Divisors

P. Erdős, Hugh L. Montgomery

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Letkbe a fixed integer,k≥2, and suppose thatε>0. We show that every sufficiently large integerncan be expressed in the formn=m1+m2+...+mkwhered(m i)>n(log2-ε)(1-1/k)/loglognfor alli. This is best possible, since there are infinitely many exceptionalnif the factor log2-εis replaced by log2+ε.

Original languageEnglish
Pages (from-to)1-6
Number of pages6
JournalJournal of Number Theory
Volume75
Issue number1
DOIs
Publication statusPublished - Mar 1999

Fingerprint

Divisor
Integer

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Sums of Numbers with Many Divisors. / Erdős, P.; Montgomery, Hugh L.

In: Journal of Number Theory, Vol. 75, No. 1, 03.1999, p. 1-6.

Research output: Contribution to journalArticle

Erdős, P. ; Montgomery, Hugh L. / Sums of Numbers with Many Divisors. In: Journal of Number Theory. 1999 ; Vol. 75, No. 1. pp. 1-6.
@article{08257e4f38b64d728dffceb9187dffa1,
title = "Sums of Numbers with Many Divisors",
abstract = "Letkbe a fixed integer,k≥2, and suppose thatε>0. We show that every sufficiently large integerncan be expressed in the formn=m1+m2+...+mkwhered(m i)>n(log2-ε)(1-1/k)/loglognfor alli. This is best possible, since there are infinitely many exceptionalnif the factor log2-εis replaced by log2+ε.",
author = "P. Erdős and Montgomery, {Hugh L.}",
year = "1999",
month = "3",
doi = "10.1006/jnth.1998.2323",
language = "English",
volume = "75",
pages = "1--6",
journal = "Journal of Number Theory",
issn = "0022-314X",
publisher = "Academic Press Inc.",
number = "1",

}

TY - JOUR

T1 - Sums of Numbers with Many Divisors

AU - Erdős, P.

AU - Montgomery, Hugh L.

PY - 1999/3

Y1 - 1999/3

N2 - Letkbe a fixed integer,k≥2, and suppose thatε>0. We show that every sufficiently large integerncan be expressed in the formn=m1+m2+...+mkwhered(m i)>n(log2-ε)(1-1/k)/loglognfor alli. This is best possible, since there are infinitely many exceptionalnif the factor log2-εis replaced by log2+ε.

AB - Letkbe a fixed integer,k≥2, and suppose thatε>0. We show that every sufficiently large integerncan be expressed in the formn=m1+m2+...+mkwhered(m i)>n(log2-ε)(1-1/k)/loglognfor alli. This is best possible, since there are infinitely many exceptionalnif the factor log2-εis replaced by log2+ε.

UR - http://www.scopus.com/inward/record.url?scp=0043046090&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0043046090&partnerID=8YFLogxK

U2 - 10.1006/jnth.1998.2323

DO - 10.1006/jnth.1998.2323

M3 - Article

AN - SCOPUS:0043046090

VL - 75

SP - 1

EP - 6

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 1

ER -