Question

Divisor Function Analytic Continuation

score 259 · Answer 1 · 2026-03-26 06:17:24

259

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Divisor Function Analytic Continuation

Published on 26 Mar 2026 - 6:17

score 130 · Answer 2 · 2026-03-26 01:23:29

130

Views

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

Published on 26 Mar 2026 - 1:23

score 90 · Answer 3 · 2026-03-25 23:36:47

90

Views

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

Published on 25 Mar 2026 - 23:36

score 57 · Answer 4 · 2026-04-14 10:44:28

57

Views

Product of All Positive Divisors of a Number

Published on 14 Apr 2026 - 10:44

score 172 · Answer 5 · 2026-03-26 01:12:38

172

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 26 Mar 2026 - 1:12

score 122 · Answer 6 · 2026-03-25 22:03:39

122

Views

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

Published on 25 Mar 2026 - 22:03

score 52 · Answer 7 · 2026-04-09 11:21:16

52

Views

Numbers of divisors for a Mersenne number

Published on 09 Apr 2026 - 11:21

score 79 · Answer 8 · 2026-03-25 22:04:41

79

Views

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

Published on 25 Mar 2026 - 22:04

score 21 · Answer 9 · 2026-03-25 23:42:17

21

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 25 Mar 2026 - 23:42

score 114 · Answer 10 · 2026-03-25 22:02:37

114

Views

Prove that φ(n) + d(n) ≤ n + 1

Published on 25 Mar 2026 - 22:02

score 73 · Answer 11 · 2026-03-26 01:02:05

73

Views

A Diophantine equation centered around the divisor counting function and squares

Published on 26 Mar 2026 - 1:02

score 46 · Answer 12 · 2026-03-26 01:12:36

46

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 26 Mar 2026 - 1:12

score 56 · Answer 13 · 2026-03-25 23:42:20

56

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 25 Mar 2026 - 23:42

score 58 · Answer 14 · 2026-04-24 22:02:08

58

Views

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

Published on 24 Apr 2026 - 22:02

score 1.6k · Answer 15 · 2026-04-11 12:41:36

1.6k

Views

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

Published on 11 Apr 2026 - 12:41

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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