MathDB

Let

A

be an infinite subset of the set of natural numbers, and denote by

\tau_A(n)

the number of divisors of

n

A

. Construct a set

A

for which

\sum_{n\le x}\tau_A(n)=x+O(\log\log x)

and show that there is no set for which the error term is

o(\log\log x)

in the above formula.
(translated by Miklós Maróti)

Problem Statement