Sums of Numbers with Many Divisors

Paul Erdos, Hugh L. Montgomery

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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 1 1999

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ASJC Scopus subject areas

  • Algebra and Number Theory

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