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Do these arithmetic functions have an infinite number of integer zeros?

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#number-theory #summation #riemann-zeta #arithmetic-functions #mobius-function
118
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Showing that the limit is $1/\varphi(q)$

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#number-theory #analytic-number-theory #arithmetic-progressions #arithmetic-functions
59
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On the biconditional $I(n^2) = 2 - \frac{5}{3q} \iff (k = 1 \land q = 5)$, where $q^k n^2$ is an odd perfect number

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#number-theory #inequality #divisor-sum #arithmetic-functions #perfect-numbers
72
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Implications of $q \neq 1049$ when $q^k n^2$ is an odd perfect number

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#inequality #divisor-sum #arithmetic-functions #perfect-numbers
738
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Sum with the von-Mangoldt function: $\sum_{1\leq x\leq n}\Lambda(x)^4$

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#analytic-number-theory #arithmetic-functions
383
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Why tetration and more are not common in nature?

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#arithmetic-functions #tetration #hyperoperation
43
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Get rid of duplicated values with basic math

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#arithmetic #arithmetic-functions
51
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Is this function an injection of $\mathbb{N} \to \mathbb{R}$?

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#sequences-and-series #summation #irrational-numbers #pi #arithmetic-functions
28
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How to reverse extrapolate values $Q$ and $C$ from arithmetic function?

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#arithmetic #arithmetic-progressions #arithmetic-functions
250
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Prove that $J_r(n) = n^r\prod_{p|n}\left(1− \frac{1}{p^r}\right)$.

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#number-theory #elementary-number-theory #prime-numbers #totient-function #arithmetic-functions
179
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Lower bound related to the number of distinct prime numbers

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#sequences-and-series #number-theory #elementary-number-theory #prime-factorization #arithmetic-functions
478
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An absolute upper bound for $\omega(n)$

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#number-theory #prime-numbers #estimation #arithmetic-functions
73
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How to prove $\sum_{d|n} \mu(\frac{n}{d}) P(d) = 1$?

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#number-theory #prime-numbers #arithmetic-functions #mobius-function
101
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An inequality for the sum-of-aliquot-divisors function

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#inequality #solution-verification #upper-lower-bounds #divisor-sum #arithmetic-functions
56
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An improved inequality for the deficiency function when $\gcd(x,y)=1$, $x > 1$, and $y > 1$

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#inequality #solution-verification #upper-lower-bounds #divisor-sum #arithmetic-functions

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