On the fractional parts of roots of positive real numbers

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Let [θ] denote the integer part and θ the fractional part of the real number θ. For θ> 1 and θ¹/ⁿ ≠ 0, define Mθ(n) = [1/θ¹/ⁿ]. The arithmetic function Mθ(n) is eventually increasing, and ₙ→ ∞ Mθ(n)/n = 1/ θ. Moreover, Mθ(n) is "linearly periodic" if and only if θis rational. Other results and problems concerning the function Mθ(n) are discussed.