MathDB

Let

1<a_1<a_2< \ldots <a_n<x

be positive integers such that \sum_{i\equal{}1}^n 1/a_i \leq 1. Let

y

denote the number of positive integers smaller that

x

not divisible by any of the

a_i

. Prove that

y > \frac{cx}{\log x}

with a suitable positive constant

c

(independent of

x

and the numbers

a_i

). I. Z. Ruzsa

Problem Statement