Divisor weighted sums
β Scribed by J. B. Friedlander; H. Iwaniec
- Publisher
- Springer US
- Year
- 2006
- Tongue
- English
- Weight
- 354 KB
- Volume
- 137
- Category
- Article
- ISSN
- 1573-8795
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π SIMILAR VOLUMES
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&1Γk)Γlog log n for all i. This is best possible, since there are infinitely many exceptional n if the factor log 2&= i
We discuss the problem of representing a natural number \(n\) as a sum of certain of its distinct positive proper \((\neq n)\) divisors. If this is possible \(n\) is called semiperfect. We present a method which leads in certain cases to a verification that all abundant numbers with prime divisors l