Abstract
We study some arithmetic properties of the Ramanujan function τ(n), such as the largest prime divisorP (τ(n)) and the number of distinct prime divisors ω (τ (n)) of τ(n) for various sequences ofn. In particular, we show thatP(τ(n)) ≥ (logn)33/31+o(1) for infinitely many n, and
for every primep with τ(ρ) ≠ 0.
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Dedicated to T N Shorey on his sixtieth birthday
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Luca, F., Shparlinski, I.E. Arithmetic properties of the Ramanujan function. Proc. Indian Acad. Sci. (Math. Sci.) 116, 1–8 (2006). https://doi.org/10.1007/BF02829735
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DOI: https://doi.org/10.1007/BF02829735