Question

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

score 66 · Answer 1 · 2026-04-29 12:48:44

66

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

Published on 29 Apr 2026 - 12:48

score 1.2k · Answer 2 · 2026-05-02 18:19:20

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 02 May 2026 - 18:19

score 235 · Answer 3 · 2026-05-03 17:38:26

235

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

Published on 03 May 2026 - 17:38

score 76 · Answer 4 · 2026-04-29 12:42:35

76

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Multiplicative arithmetic function on the unit disk

Published on 29 Apr 2026 - 12:42

score 64 · Answer 5 · 2026-05-04 03:59:07

64

Views

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

Published on 04 May 2026 - 3:59

score 197 · Answer 6 · 2026-05-03 08:51:56

197

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 03 May 2026 - 8:51

score 112 · Answer 7 · 2026-04-29 12:24:25

112

Views

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

Published on 29 Apr 2026 - 12:24

score 345 · Answer 8 · 2026-05-04 04:14:42

345

Views

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

Published on 04 May 2026 - 4:14

score 68 · Answer 9 · 2026-04-29 12:49:52

68

Views

Inverse of a Multiplicative Arithmetic Function w/0 Mobius function

Published on 29 Apr 2026 - 12:49

score 38 · Answer 10 · 2026-04-29 12:50:18

38

Views

Inverting arithmetic functions

Published on 29 Apr 2026 - 12:50

score 67 · Answer 11 · 2026-05-03 08:48:55

67

Views

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

Published on 03 May 2026 - 8:48

score 57 · Answer 12 · 2026-04-23 02:36:44

57

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 23 Apr 2026 - 2:36

score 203 · Answer 13 · 2026-04-23 23:04:59

203

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 23 Apr 2026 - 23:04

score 204 · Answer 14 · 2026-04-24 01:11:21

204

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

Published on 24 Apr 2026 - 1:11

score 119 · Answer 15 · 2026-04-23 16:24:19

119

Views

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

Published on 23 Apr 2026 - 16:24

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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