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Möbius function for prime $p$ and gcd of prime $p$ and $d$ where $d$ divides $n$

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#discrete-mathematics #prime-numbers #mobius-function
206
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Squarefree totient sum

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#number-theory #summation #analytic-number-theory #totient-function #mobius-function
175
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Convolving the relation $o(x)$

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#number-theory #asymptotics #mobius-function
148
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Is there an unlimited number of sequences of consecutive numbers with $\mu(n)=0$ of any length?

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#sequences-and-series #elementary-number-theory #mobius-function
54
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Solutions to the following equation including a Mobius function

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#number-theory #derivatives #algorithms #mobius-function
131
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Sums of Möbius between $x$ and $y$

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#number-theory #elementary-number-theory #mobius-function #mobius-inversion
105
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Showing $\mu(n) = \sum_{k} e^{2\pi \frac{k}{n} i}$ using cosine explanation

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#number-theory #analysis #mobius-function
166
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Dirichlet convolution of Mobius function with exponential function

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#sequences-and-series #analytic-number-theory #mobius-function #dirichlet-convolution
67
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Möbius function of a linearly (totally) ordered set

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#combinatorics #recursion #mobius-function
110
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Do these multiplicative functions exist?

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#number-theory #prime-factorization #roots-of-unity #mobius-function #multiplicative-function
235
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Show that, $(-1)^{\mu(1)}+(-1)^{\mu(2)}+...+(-1)^{\mu(n)}<0$ and proof on conjecture of OEIS A209802

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#analytic-number-theory #mobius-function
104
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Is this relation already discovered?

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#number-theory #elementary-number-theory #reference-request #multinomial-coefficients #mobius-function
102
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For $a(n)=\sum\limits_{d|n}\mu(d)\ \mu\left(\frac{n}{d}\right)$, does $\underset{x\to\infty}{\text{lim}}\left(\sum_{n=1}^x\frac{a(n)}{n}\right)=0$?

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#sequences-and-series #number-theory #arithmetic-functions #mobius-function
161
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Solve the equation with respect to $k_1,k_2\in \mathbb{Z}_{+}$

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#combinatorics #number-theory #discrete-mathematics #mobius-function
89
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A question related to behavior of mobius function $\mu(d)$

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#number-theory #summation #analytic-number-theory #mobius-function

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