Summary: For any positive integer \(n\), define \(H (1)=1\) and \(H (n)=\frac 1{p_1}+\frac 1{p_2}+\cdots +\frac 1{p_k}\) if \(n>1\), and \(n=p^{\alpha_1}_1 p^{\alpha_2}_2\cdots p^{\alpha_k}_k\), which decomposes \(n\) into prime powers, let \(p (n)\) be the smallest prime divisor of \(n\). The main purpose of this paper is using the elementary methods to study the value distribution properties of \(H (P_d (n))\) and \(H (q_d (n))\), and give four sharp asymptotic formulae for it.