Arithmetic Functions and the Euler Phi Function
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چکیده
• An arithmetic function takes positive integers as inputs and produces real or complex numbers as outputs. • If f is an arithmetic function, the divisor sum Df(n) is the sum of the values of f at the positive divisors of n. • τ (n) is the number of positive divisors of n; σ(n) is the sum of the positive divisors of n. • The Möbius function μ(n) is 1 if n = 1 and 0 if n has a repeated prime factor. Otherwise, it is (−1), where k is the number of (distinct) prime factors. • The Dirichlet product of arithmetic functions f and g is (f ∗ g)(n) = ∑
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