Divisors of Bernoulli Sums

✍ Michel Weber 📂 Article 📅 2009 🏛 Springer 🌐 English ⚖ 373 KB

Divisor weighted sums

✍ J. B. Friedlander; H. Iwaniec 📂 Article 📅 2006 🏛 Springer US 🌐 English ⚖ 354 KB

Sums of Numbers with Many Divisors

✍ Paul Erdős; Hugh L Montgomery 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 87 KB

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&= i

Sums of Divisors and Egyptian Fractions

✍ C.N. Friedman 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 470 KB

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

Sums of Products of Bernoulli Numbers

✍ Karl Dilcher 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 573 KB

Closed expressions are obtained for sums of products of Bernoulli numbers of the form ( 2n 2j 1 , ..., 2jN ) B 2j1 } } } B 2jN , where the summation is extended over all nonnegative integers j 1 , ..., j N with j 1 + j 2 + } } } + j N =n. Corresponding results are derived for Bernoulli polynomials,

On divisors of sums of integers. I

✍ A. Sárközy; C. L. Stewart 📂 Article 📅 1986 🏛 Akadmiai Kiad 🌐 English ⚖ 308 KB