  Let $n$ and $k$ be positive integers. The Stirling number of the first kind,
denoted by $s(n,k)$, counts the number of permutations of $n$ elements with $k$
disjoint cycles. Let $p$ be a prime number and denote by $v_p(n)$ the $p$-adic
valuation of $n$. In recent years, Lengyel, Komatsu, Young, Leonetti and Sanna
made some progress on $v_p(s(n,k))$. Let $a\in\{1,2\}$. In this paper, by using
the properties of $m$-th Stirling number of the first kind developed previously
and providing a detailed 3-adic analysis, we arrive at an explicit formula on
$v_3(s(a3^n, k))$ with $1\le k\le a3^n$. This gives an evidence to a conjecture
of Hong and Qiu proposed in 2020. As a corollary, we show that
$v_3(s(a3^n,a3^n-k))=2n-1+v_3(k)-v_3(k-1)$ if $k$ is odd and $3\le k\le
a3^{n-1}+1$. This supports a conjecture of Lengyel raised in 2015.
