✦ LIBER ✦

On the sum of Divisors Function

✍ Scribed by U. Balakrishnan

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 484 KB
Volume: 51
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1995.1041

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

Note on sums containing small divisors

✍ Helmut Rüßmann 📂 Article 📅 1976 🏛 John Wiley and Sons 🌐 English ⚖ 112 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

On the Smallest Divisor of a Polynomial

✍ Maurice Mignotte; Philippe Glesser 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 129 KB

On an Inequality for the Sum of Infimums

On an Inequality for the Sum of Infimums of Functions

✍ J. Sándor; V.E.S. Szabó 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 123 KB

In this paper we prove some known and new inequalities using an elementary inequality and some basic facts from differential calculus.

On the Proximity of Algebraic Units To D

On the Proximity of Algebraic Units To Divisors

✍ G.R. Everest 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 493 KB

An asymptotic formula counting algebraic units with respect to a proximity function on the group variety is given. The proximity function measures the local distance to a divisor on the variety. The formula allows a natural definition of mean distance between the group and the divisor. By allowing t