Question

Find all $f$ such that $\sum_{d|n}f(d)=\varphi(n)$

score 130 · Answer 1 · 2026-04-15 21:57:46

130

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Find all $f$ such that $\sum_{d|n}f(d)=\varphi(n)$

Published on 15 Apr 2026 - 21:57

score 216 · Answer 2 · 2026-04-16 14:00:32

216

Views

If $d$ is the order of $a$ modulo $n$ then prove that $n| \Phi_d(a)$

Published on 16 Apr 2026 - 14:00

score 571 · Answer 3 · 2026-04-17 13:02:44

571

Views

Asymptotic or Exact formula for Harmonic Number

Published on 17 Apr 2026 - 13:02

score 205 · Answer 4 · 2026-04-15 17:10:13

205

Views

Brainstorming to search links between $\pi(x)$ and the convexity of $-\int_2^x\frac{dt}{\log(t)}$, related to the Second Hardy–Littlewood conjecture

Published on 15 Apr 2026 - 17:10

score 163 · Answer 5 · 2026-03-27 06:12:36

163

Views

What about the convergence of $\sum_{n=1}^\infty\frac{(\mu(n))^n}{n}$, where $\mu(n)$ is the Möbius function?

Published on 27 Mar 2026 - 6:12

score 79 · Answer 6 · 2026-04-15 17:48:54

79

Views

On functions that satisfy $\int_0^1\frac{f(x)}{1-x}dx<\infty$ as a version of the Prime Number Theorem for the Möbius function

Published on 15 Apr 2026 - 17:48

score 77 · Answer 7 · 2026-04-14 00:28:55

77

Views

Treasures from the OEIS Plot 2

Published on 14 Apr 2026 - 0:28

score 49 · Answer 8 · 2026-04-16 15:55:50

49

Views

An estimation of the number of prime in the form $4n+3$?

Published on 16 Apr 2026 - 15:55

score 47 · Answer 9 · 2026-04-16 07:35:51

47

Views

Bounding the number of polynomials in $\mathbb{F}_p$ where its discriminant is divisible by some fix prime number $p$.

Published on 16 Apr 2026 - 7:35

score 29 · Answer 10 · 2026-03-26 03:01:37

29

Views

What is the "sieve and limiting process" technique? (From a paper of Ërdos on polynomials with power-free values)

Published on 26 Mar 2026 - 3:01

score 153 · Answer 11 · 2026-04-15 14:55:28

153

Views

Can we imagine some strange "unit" $ S $ such that $ S \times 0 = 1 $?

Published on 15 Apr 2026 - 14:55

score 723 · Answer 12 · 2026-04-14 15:07:52

723

Views

On Siegel mass formula

Published on 14 Apr 2026 - 15:07

score 225 · Answer 13 · 2026-04-14 06:18:36

225

Views

Partial sum of harmonic series, every n is coprime to some k

Published on 14 Apr 2026 - 6:18

score 54 · Answer 14 · 2026-04-16 09:35:25

54

Views

Möbius function and the independence of a sequence of random variables which is either i.i.d with null expectation, the product of such vars, or zero

Published on 16 Apr 2026 - 9:35

score 147 · Answer 15 · 2026-04-09 08:34:39

147

Views

How to prove that: $2e^{-2x}(e^x -1)= \displaystyle\sum_{n=1}^\infty \frac{\mu(n)}{\sinh(nx)}$

Published on 09 Apr 2026 - 8:34

List Question

Find all $f$ such that $\sum_{d|n}f(d)=\varphi(n)$

If $d$ is the order of $a$ modulo $n$ then prove that $n| \Phi_d(a)$

Asymptotic or Exact formula for Harmonic Number

Brainstorming to search links between $\pi(x)$ and the convexity of $-\int_2^x\frac{dt}{\log(t)}$, related to the Second Hardy–Littlewood conjecture

What about the convergence of $\sum_{n=1}^\infty\frac{(\mu(n))^n}{n}$, where $\mu(n)$ is the Möbius function?

On functions that satisfy $\int_0^1\frac{f(x)}{1-x}dx<\infty$ as a version of the Prime Number Theorem for the Möbius function

Treasures from the OEIS Plot 2

An estimation of the number of prime in the form $4n+3$?

Bounding the number of polynomials in $\mathbb{F}_p$ where its discriminant is divisible by some fix prime number $p$.

What is the "sieve and limiting process" technique? (From a paper of Ërdos on polynomials with power-free values)

Can we imagine some strange "unit" $ S $ such that $ S \times 0 = 1 $?

On Siegel mass formula

Partial sum of harmonic series, every n is coprime to some k

Möbius function and the independence of a sequence of random variables which is either i.i.d with null expectation, the product of such vars, or zero

How to prove that: $2e^{-2x}(e^x -1)= \displaystyle\sum_{n=1}^\infty \frac{\mu(n)}{\sinh(nx)}$

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