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Prove $\lambda(n)=\sum_{d^2|n}\mu(n/d)^2$ and $\mu^2(n)=\sum_{d^2|n}\mu(d)$

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#number-theory #arithmetic-functions #multiplicative-function #mobius-function #liouville-function
604
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Proving an identity of the Möbius function and Euler’s totient function product

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#elementary-number-theory #arithmetic-functions
572
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Lower bound of Euler phi function times sum of divisors

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#number-theory #inequality #totient-function #arithmetic-functions
545
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Summing the reciprocal of $\phi(n)^2$

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#analytic-number-theory #arithmetic-functions
122
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Arithmetic functions used in number theory

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#functions #reference-request #prime-numbers #arithmetic-functions
106
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Can we improve on the inequality $\sigma(N)\varphi(N) < N^2$ for integers $N > 1$?

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#inequality #totient-function #divisor-sum #arithmetic-functions
40
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multiple sums including moebius mu function?

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#number-theory #elementary-number-theory #summation #arithmetic-functions #multiplicative-function
400
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Multiplication with negative multiplier

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#arithmetic #arithmetic-functions
83
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Natural numbers $n$ satisfying $\mu(n+1)+\mu(n+2)+\cdots+\mu(n+2019)=2019$

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#elementary-number-theory #summation #arithmetic-functions
90
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Prove that $\sum_{n\leq x}{d(\phi(n))} > x \log{x}$

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#number-theory #analytic-number-theory #arithmetic-functions
67
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Proving that $g(1) = 1$, where $g$ is a multiplicative arithmetic function

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#elementary-number-theory #arithmetic-functions #multiplicative-function
222
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Does normal order imply average order?

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#number-theory #elementary-number-theory #analytic-number-theory #arithmetic-functions
48
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arithmetic function invertible concerning convolution?

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#elementary-number-theory #inverse #convolution #arithmetic-functions
70
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A possible disproof for the Descartes-Frenicle-Sorli Conjecture on odd perfect numbers

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#proof-verification #conjectures #divisor-sum #arithmetic-functions #perfect-numbers
121
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determining a convolution of an arithmetic function

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#number-theory #elementary-number-theory #arithmetic-functions #dirichlet-convolution

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