Arithmetic properties of the Ramanujan function

2006/07/24 by Luca, Florian, Shparlinski, Igor E
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.math/0607591

Abstract

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 \hboxP(τ(n)) ≥ (log n)^{33/31 + o(1)} for infinitely many n, and P(τ(p)τ(p²)τ(p³)) gt; (1+o(1))\fracloglog plogloglog p loglogloglog p for every prime p with \hboxτ(p)≠ 0.

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