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Sums of Numbers with Many Divisors

✍ Scribed by Paul Erdős; Hugh L Montgomery

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
87 KB
Volume
75
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let k be a fixed integer, k 2, and suppose that =>0. We show that every sufficiently large integer n can be expressed in the form n=m 1 +m 2 + } } } +m k where d(m i )>n (log 2&=)(1&1Âk)Âlog log n for all i. This is best possible, since there are infinitely many exceptional n if the factor log 2&= is replaced by log 2+=.

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