On Number of Integers Representable as Sums of Unit Fractions

Abstract

Let N(n) be the set of all integers that can be written in the form where ∊(n) → 0 as n → ∞, answering a question of P. Erdös and R. L. Graham.

On Number of Integers Representable as a Sum of Unit Fractions, II

“…Concerning the lower bound of |N(n)|, Erdo s and Graham [1] asked whether |N(n)| =O(log n). This question was settled by the author [5]. He showed that |N(n)| ( 1 2 &=(n)) log n, where =(n) Ä 0 as n Ä .…”

The Largest Integer Expressible as a Sum of Reciprocal of Integers

“…Concerning the order of |N(n)|, P. Erdo s and R. L. Graham [1] asked whether |N(n)| > >log n. This question was settled by the author [7]. He showed that \ 1 2 & log 2 n log n + log n |N(n)| log n+1.…”

On the Number of Integers Representable as Sums of Unit Fractions, III

“…where e k takes either 0 or 1: Answering questions of Erd + o os and Graham [5], we have shown (see [10][11][12][13]) that log n þ g À 2 À oð1Þ4jNðnÞj4log n þ g À 1 4 þ oð1Þ ðlog 2 nÞ 2 log n :…”