Hardy-Ramanujan Journal |
Let ωy(n) denote the number of distinct prime divisors of n less than y. Suppose yn is an increasing sequence of positive real numbers satisfying logyn=o(loglogn). In this paper, we prove an Erdös-Kac theorem for the distribution of ωyn(p+a), where p runs over all prime numbers and a is a fixed integer. We also highlight the connection between the distribution of ωy(p−1) and Ihara's conjectures on Euler-Kronecker constants.