Question

Prove the asymptotic probability of numbers being relative prime equals $\frac{6}{\pi^2}$

score 61 · Answer 1 · 2026-03-23 09:29:59

61

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Prove the asymptotic probability of numbers being relative prime equals $\frac{6}{\pi^2}$

Published on 23 Mar 2026 - 9:29

score 1.2k · Answer 2 · 2026-03-23 03:04:36

1.2k

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Prove $ \left\vert \sum_{n=1}^N \frac{\mu(n)}{n} \right\vert \leqslant 1,$ where $\mu(n)$ is the Mobius function.

Published on 23 Mar 2026 - 3:04

score 225 · Answer 3 · 2026-03-22 14:40:38

225

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$Var[w]=O(\log\log(N))$ where $w(n)$ is the no of prime divisors of $n$

Published on 22 Mar 2026 - 14:40

score 68 · Answer 4 · 2026-03-20 05:41:05

68

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Multiplicative arithmetic function on the unit disk

Published on 20 Mar 2026 - 5:41

score 56 · Answer 5 · 2026-03-22 23:16:36

56

Views

Is feasible a simple inequality as a combination of the Firoozbakht's conjecture and the properties of the Ramanujan tau function?

Published on 22 Mar 2026 - 23:16

score 191 · Answer 6 · 2026-03-22 18:12:33

191

Views

Is it true that $\underbrace{x^{x^{x^{.^{.^{.^x}}}}}}_{k\,\text{times}}\pmod9$ has period $18$ and can never take the values $3$ and $6$?

Published on 22 Mar 2026 - 18:12

score 102 · Answer 7 · 2026-03-22 19:09:51

102

Views

Is the average order of a product of arithmetic functions the product of the average orders?

Published on 22 Mar 2026 - 19:09

score 336 · Answer 8 · 2026-03-22 19:03:47

336

Views

If $f$ is an arithmetic function with $f(1)=1$ then $f$ is multiplicative

Published on 22 Mar 2026 - 19:03

score 62 · Answer 9 · 2026-03-22 23:17:46

62

Views

Inverse of a Multiplicative Arithmetic Function w/0 Mobius function

Published on 22 Mar 2026 - 23:17

score 31 · Answer 10 · 2026-03-23 03:57:59

31

Views

Inverting arithmetic functions

Published on 23 Mar 2026 - 3:57

score 58 · Answer 11 · 2026-03-10 12:53:20

58

Views

Deduce the number of divisors, $d(n)$ is multiplicative and obtain a formula of $d(n)$ in terms of prime decomposition

Published on 10 Mar 2026 - 12:53

score 54 · Answer 12 · 2026-03-25 03:04:05

54

Views

Does $D(n)$ always depend on $\gcd(n,\sigma(n))$ when $\sigma(N)=aN+b$, $N=xn$, and $n$ is a square?

Published on 25 Mar 2026 - 3:04

score 200 · Answer 13 · 2026-03-25 04:43:47

200

Views

A bound for a sum over square-free numbers: $\sum_{n \leq X} \frac{\mu(n)^2 \tau_k(n)}{\phi(n)} \ll (\log X)^k$

Published on 25 Mar 2026 - 4:43

score 201 · Answer 14 · 2026-03-25 03:07:31

201

Views

Do odd numbers $n$ satisfying $\gcd(n, \sigma(n)) > \sqrt{n}$ have a special form?

Published on 25 Mar 2026 - 3:07

score 116 · Answer 15 · 2026-03-25 04:41:32

116

Views

Is there a lower bound for $\operatorname{rad}(n)$ in terms of $n \in \mathbb{N}$?

Published on 25 Mar 2026 - 4:41

List Question

Prove the asymptotic probability of numbers being relative prime equals $\frac{6}{\pi^2}$

Prove $ \left\vert \sum_{n=1}^N \frac{\mu(n)}{n} \right\vert \leqslant 1,$ where $\mu(n)$ is the Mobius function.

$Var[w]=O(\log\log(N))$ where $w(n)$ is the no of prime divisors of $n$

Multiplicative arithmetic function on the unit disk

Is feasible a simple inequality as a combination of the Firoozbakht's conjecture and the properties of the Ramanujan tau function?

Is it true that $\underbrace{x^{x^{x^{.^{.^{.^x}}}}}}_{k\,\text{times}}\pmod9$ has period $18$ and can never take the values $3$ and $6$?

Is the average order of a product of arithmetic functions the product of the average orders?

If $f$ is an arithmetic function with $f(1)=1$ then $f$ is multiplicative

Inverse of a Multiplicative Arithmetic Function w/0 Mobius function

Inverting arithmetic functions

Deduce the number of divisors, $d(n)$ is multiplicative and obtain a formula of $d(n)$ in terms of prime decomposition

Does $D(n)$ always depend on $\gcd(n,\sigma(n))$ when $\sigma(N)=aN+b$, $N=xn$, and $n$ is a square?

A bound for a sum over square-free numbers: $\sum_{n \leq X} \frac{\mu(n)^2 \tau_k(n)}{\phi(n)} \ll (\log X)^k$

Do odd numbers $n$ satisfying $\gcd(n, \sigma(n)) > \sqrt{n}$ have a special form?

Is there a lower bound for $\operatorname{rad}(n)$ in terms of $n \in \mathbb{N}$?

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