Question

Divisor Function Analytic Continuation

score 258 · Answer 1 · 2026-03-22 17:37:42

258

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Divisor Function Analytic Continuation

Published on 22 Mar 2026 - 17:37

score 129 · Answer 2 · 2023-03-02 12:58:13

129

Views

Number of Divisors of $m$ Such That They're All Less Than Some $n$

Published on 02 Mar 2023 - 12:58

score 89 · Answer 3 · 2023-04-11 07:32:25

89

Views

Asymptotic on $\sum_{n<x} 1/d_{\alpha}(n)$, $d_\alpha$ is the general divisor function.

Published on 11 Apr 2023 - 7:32

score 54 · Answer 4 · 2023-04-19 18:05:30

54

Views

Product of All Positive Divisors of a Number

Published on 19 Apr 2023 - 18:05

score 171 · Answer 5 · 2023-06-04 00:30:29

171

Views

Call $n\in\Bbb N$ "balanced" if the sum of its digits equals the count of its divisors. How many "balanced" numbers are there up to $m$?

Published on 04 Jun 2023 - 0:30

score 121 · Answer 6 · 2023-06-07 20:47:15

121

Views

Proving that there are infinite primes with digit sum 8 in base 10

Published on 07 Jun 2023 - 20:47

score 51 · Answer 7 · 2026-02-23 04:59:06

51

Views

Numbers of divisors for a Mersenne number

Published on 23 Feb 2026 - 4:59

score 78 · Answer 8 · 2023-08-29 22:30:31

78

Views

Dirichlet series of $\ln(n) \tau(n)$

Published on 29 Aug 2023 - 22:30

score 20 · Answer 9 · 2023-10-02 09:59:58

20

Views

Solve $0=(u^2+v^2)^{\frac12}\left(u\sum_{n=1}^{\infty}\sigma_3(n)ny^n\cos(t-nz)+v\sum_{n=1}^{\infty}\sigma_3(n)ny^n\sin(t+nz)\right)$ for $t$

Published on 02 Oct 2023 - 9:59

score 113 · Answer 10 · 2023-10-12 13:14:57

113

Views

Prove that φ(n) + d(n) ≤ n + 1

Published on 12 Oct 2023 - 13:14

score 72 · Answer 11 · 2023-12-08 10:09:31

72

Views

A Diophantine equation centered around the divisor counting function and squares

Published on 08 Dec 2023 - 10:09

score 45 · Answer 12 · 2024-02-21 15:40:29

45

Views

Solutions of equations of form $\tau(n+a_i)=\tau(x+a_i)$ where $\tau$ is the number of divisors function and $a_i$ is a diverging series

Published on 21 Feb 2024 - 15:40

score 55 · Answer 13 · 2024-02-28 09:51:34

55

Views

On the "efficiency" of digit-sum divisibility tricks in other bases (or about the growth rate of the number of divisors function).

Published on 28 Feb 2024 - 9:51

score 44 · Answer 14 · 2026-03-25 01:53:57

44

Views

Can we detect a highly composite number and determine its number in the list?

Published on 25 Mar 2026 - 1:53

score 1.6k · Answer 15 · 2026-02-23 19:38:08

1.6k

Views

How many number between 1 and 1000 satisfy a certain condition?

Published on 23 Feb 2026 - 19:38

List Question

Divisor Function Analytic Continuation

Number of Divisors of $m$ Such That They're All Less Than Some $n$

Asymptotic on $\sum_{n<x} 1/d_{\alpha}(n)$, $d_\alpha$ is the general divisor function.

Product of All Positive Divisors of a Number

Call $n\in\Bbb N$ "balanced" if the sum of its digits equals the count of its divisors. How many "balanced" numbers are there up to $m$?

Proving that there are infinite primes with digit sum 8 in base 10

Numbers of divisors for a Mersenne number

Dirichlet series of $\ln(n) \tau(n)$

Solve $0=(u^2+v^2)^{\frac12}\left(u\sum_{n=1}^{\infty}\sigma_3(n)ny^n\cos(t-nz)+v\sum_{n=1}^{\infty}\sigma_3(n)ny^n\sin(t+nz)\right)$ for $t$

Prove that φ(n) + d(n) ≤ n + 1

A Diophantine equation centered around the divisor counting function and squares

Solutions of equations of form $\tau(n+a_i)=\tau(x+a_i)$ where $\tau$ is the number of divisors function and $a_i$ is a diverging series

On the "efficiency" of digit-sum divisibility tricks in other bases (or about the growth rate of the number of divisors function).

Can we detect a highly composite number and determine its number in the list?

How many number between 1 and 1000 satisfy a certain condition?

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