On the distribution of a linear sequence associated to sum of divisors evaluated at polynomial arguments (Q2856770)

In the article under review, the author considers sequences involving the sum of divisors function. The main tool in the proof is a sieving argument.NEWLINENEWLINEWe call a sequence \((a_n)_{n\geq1}\) dense modulo 1 if the sequence of its fractional parts \((\{a_n\})_{n\geq1}\) is dense in the interval \([0,1)\). Let \(\sigma(m)=\sum_{d\mid m}d\) denote the sum of divisors of \(m\). Then for \(m\geq1\) we set NEWLINE\[NEWLINEs_m:=\frac{m^2+2}{\sigma(m^2+1)}.NEWLINE\]NEWLINE The author's main result states that the sequence \((b_n)_{n\geq1}\) with \(b_n=\sum_{m\leq n}s_m\) is dense modulo 1.