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Denote by Ω(n) the number of prime divisors of n ∈ ℕ (counted with multiplicities). For x∈ ℕ define the Dirichlet-Bohr radius L(x) to be the best r > 0 such that for every finite Dirichlet polynomial ${\sum }_{n\le x}{a}_n{n}^{-s}$ we have ${\sum }_{n\le x}|a_n|r^{\Omega \left(n\right)}\le su{p}_{t\in ℝ}\left|{\sum }_{n\le x}{a}_n{n}^{-it}\right|$. We prove that the asymptotically correct order of L(x) is ${\left(logx\right)}^{1/4}{x}^{-1/8}$. Following Bohr’s vision our proof links the estimation of L(x) with classical Bohr radii for holomorphic functions in several variables. Moreover, we suggest a general setting which allows translating various results on Bohr...