On a problem of Pongsriiam on the sum of divisors, II

For any positive integer $n$, let $\sigma (n)$ be the sum of all positive divisors of $n\mathrm{.}$ In this paper, it is proved that the set of positive integers $n$ for which $\sigma (30n+1)\ge \sigma (30n)$ has a density less than $0.0371813,$ which answers a recent problem of Pongsriiam in part.