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$f$ is multiplicative $\implies f^{-1}$ is multiplicative.

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#elementary-number-theory #multiplicative-function #dirichlet-convolution
131
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Does equal Bell series imply Dirichlet convolution?

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#number-theory #elementary-number-theory #solution-verification #analytic-number-theory #dirichlet-convolution
99
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direct computation of inverse of Dirichlet convolution

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#analytic-number-theory #dirichlet-convolution
116
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Let $f:\Bbb{N}\to\Bbb{C}$ denotes the indicator function of squares. Express it in terms of Mobious function $\mu$.

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#number-theory #analytic-number-theory #arithmetic-functions #multiplicative-function #dirichlet-convolution
67
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Necessary and sufficient condition to be completely multiplicative

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#number-theory #dirichlet-series #multiplicative-function #dirichlet-convolution
173
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Product form of a Dirichlet convolution

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#number-theory #dirichlet-convolution
298
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A question about the property of completely multiplicative functions

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#number-theory #multiplicative-function #dirichlet-convolution
39
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Term-wise product of arithmetic functions and its Dirichlet generating function

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#number-theory #generating-functions #dirichlet-series #dirichlet-convolution
90
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What is the Dirichlet Convolution of the identity function with itself?

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#number-theory #divisor-counting-function #dirichlet-convolution
70
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Claim: The Euler's totient function is unique with the following property

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#solution-verification #totient-function #dirichlet-convolution
43
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Count non-decreasing sequences of a given length N made from multiples under a limit M

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#combinatorics #number-theory #divisor-counting-function #dirichlet-convolution
61
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Dirichlet's Series - Convergence

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#number-theory #dirichlet-series #dirichlet-convolution
98
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Which arithmetic functions satisfy $\sum_{d \mid n} f(\frac{n}{d}) k^d \equiv 0 \pmod{n}$ for all positive integers $n,k$?

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#number-theory #elementary-number-theory #totient-function #arithmetic-functions #dirichlet-convolution
49
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Characterization of Möbius-monotonicity

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#analytic-number-theory #arithmetic-functions #mobius-function #mobius-inversion #dirichlet-convolution
49
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What is the Dirichlet serie of The function $A$ (OEIS A001414) which gives the sum of prime factors (with repetition) of a number $n$?

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#number-theory #arithmetic-functions #dirichlet-series #mobius-function #dirichlet-convolution

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