A study of a curious arithmetic function

2010/04/13 by Bakir Farhi, Farhi, Bakir
Mathematics · #11A05 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A05

paper · pdf · doi:10.48550/arxiv.1004.2269

To appear

arxiv created 2010/04/13 · arxiv updated 2010/04/15

Abstract

In this note, we study the arithmetic function f : ℤ₊^* → ℚ₊^* defined by f(2^k ℓ) = ℓ^{1 - k} (∀ k, ℓ ∈ ℕ, ℓ odd). We show several important properties about that function and then we use them to obtain some curious results involving the 2-adic valuation.

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