  Let $\omega^*(n)$ be the number of primes $p$ such that $p-1$ divides $n$.
Assuming the Elliott--Halberstam Conjecture, we prove a conjecture posted by M.
R. Murty and V. K. Murty in 2021 which states that $$\sum_{n\leqslant
x}\omega^*(n)^2\sim 2\frac{\zeta(2)\zeta(3)}{\zeta(6)}x\log x, \quad \text{as}
\quad x\rightarrow \infty.$$ The above sum was first investigated by Prachar in
1955.
  One of the key ingredients in our argument is the application of a sieve
result on estimating various certain summations involving primes in arithmetic
progressions, rather than a direct use of the Brun--Titchmarsh inequality which
would not be applicable for our task.
