List questions from arithmetic-functions

Published on 12 Mar 2015 - 4:50

809

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Convolution identity involving the Möbius function $\sum_{d|n,d>0} |\mu(d)| = 2^{\omega(n)}$

Published on 25 Mar 2026 - 17:45

121

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The probability that a random integer is prime to a given integer $m$ is $\frac{\phi(m)}m$?

Published on 29 Mar 2015 - 14:36

221

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how to show $\lim \sup_{n \to \infty} \frac{\phi(n+1)}{\phi(n)}= \infty$ and $\lim \inf_{n \to \infty} \frac{\phi(n+1)}{\phi(n)}= 0$?

Published on 31 Mar 2015 - 13:13

156

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On the sets $\{\dfrac {\phi(n+1)}{\phi(n)} : n\in \mathbb Z^+\}$ and $\{\dfrac {\phi(n)}{n} : n\in \mathbb Z^+\}$

Published on 31 Mar 2015 - 13:32

2k

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Find all positive integers $n$ such that $\phi(n)+\sigma(n)=2n$.

Published on 01 Apr 2015 - 3:01

919

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To prove $\phi(mn)\phi(d)=\phi(m)\phi(n)d$ without explicitly computing the phi function values

Published on 01 Apr 2015 - 12:33

131

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A question about Euler's totient function

Published on 05 Apr 2015 - 23:12

46

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Multiplicative Function Property

Published on 09 Apr 2015 - 2:49

100

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Number of Divisors of most numbers

Published on 26 Mar 2026 - 1:03

304

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Summation of a function 2

Published on 26 Mar 2026 - 19:15

57

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for which values of the pair of integers $(n,k)$ is $p(n,k) =1+\frac{2^{k}-1}n$ is prime?

Published on 25 May 2015 - 22:13

951

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Bezout Coefficient for polynomials in sage?

Published on 26 Mar 2026 - 17:18

130

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If an arithmetic function has a strong logarithmic mean value, then it has an ordinary mean value.

Published on 30 May 2015 - 20:07

63

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For all $n\in\Bbb N$ does there exist $n_1$ and $n_2$ such that $d(n_1) +d(n_2)=n$

Published on 23 Jun 2015 - 2:30

List Question

Proof involving the Euler phi-function

Convolution identity involving the Möbius function $\sum_{d|n,d>0} |\mu(d)| = 2^{\omega(n)}$

The probability that a random integer is prime to a given integer $m$ is $\frac{\phi(m)}m$?

how to show $\lim \sup_{n \to \infty} \frac{\phi(n+1)}{\phi(n)}= \infty$ and $\lim \inf_{n \to \infty} \frac{\phi(n+1)}{\phi(n)}= 0$?

On the sets $\{\dfrac {\phi(n+1)}{\phi(n)} : n\in \mathbb Z^+\}$ and $\{\dfrac {\phi(n)}{n} : n\in \mathbb Z^+\}$

Find all positive integers $n$ such that $\phi(n)+\sigma(n)=2n$.

To prove $\phi(mn)\phi(d)=\phi(m)\phi(n)d$ without explicitly computing the phi function values

A question about Euler's totient function

Multiplicative Function Property

Number of Divisors of most numbers

Summation of a function 2

for which values of the pair of integers $(n,k)$ is $p(n,k) =1+\frac{2^{k}-1}n$ is prime?

Bezout Coefficient for polynomials in sage?

If an arithmetic function has a strong logarithmic mean value, then it has an ordinary mean value.

For all $n\in\Bbb N$ does there exist $n_1$ and $n_2$ such that $d(n_1) +d(n_2)=n$

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