Arithmetic properties of the Ramanujan function

We study some arithmetic properties of the Ramanujan function τ (n), such as the largest prime divisor P(τ(n)) and the number of distinct prime divisors ω(τ(n)) of τ(n) for various sequences of n. In particular, we show that P(τ(n)) ≥ (log n)^33/31+o(1) for infinitely many n, and P (τ)(p)τ(p²)τ(p ³))>(1 + o(1))log log p log log log p / log log log log p for every prime p with τ(p) ≠ 0.