Arithmetic properties of the Ramanujan function

Florian Luca*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1-8
Number of pages8
JournalProceedings of the Indian Academy of Sciences: Mathematical Sciences
Issue number1
Publication statusPublished - Feb 2006


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