Question

With $s(n)=\sum_{k=1}^n n \bmod k$, can be justified that $\forall\epsilon>0$ let us $\lim_{n\to\infty}\frac{s(n-1)}{\epsilon+s(n)}=1?$

score 77 · Answer 1 · 2015-11-25 15:32:58

77

Views

With $s(n)=\sum_{k=1}^n n \bmod k$, can be justified that $\forall\epsilon>0$ let us $\lim_{n\to\infty}\frac{s(n-1)}{\epsilon+s(n)}=1?$

Published on 25 Nov 2015 - 15:32

score 100 · Answer 2 · 2015-11-29 11:02:04

100

Views

Hints to compute if exists $\lim_{n\to\infty}\sum_{k=1}^n\sigma(k^2)/\sum_{k=1}^n\sigma(k)$, which $\sigma(n)=\sum_{d\mid n}d$, and other question

Published on 29 Nov 2015 - 11:02

score 328 · Answer 3 · 2026-03-12 16:38:21

328

Views

Please, help to identify this numerical constant

Published on 12 Mar 2026 - 16:38

score 495 · Answer 4 · 2026-03-18 23:56:59

495

Views

Trilogarithm $\operatorname{Li}_3(z)$ and the imaginary golden ratio $i\,\phi$

Published on 18 Mar 2026 - 23:56

score 70 · Answer 5 · 2015-12-18 13:52:24

70

Views

For $n\geq 1$, $\sum_{k=0}^{\infty}\frac{(-1)^{k}(nk+1)^{3}}{(k+1)^6}$ in terms of $\zeta(3)$ and $\zeta(5)$ from a series calculator. Is possible?

Published on 18 Dec 2015 - 13:52

score 822 · Answer 6 · 2015-12-20 22:14:51

822

Views

Conjecture $\int_0^1\ln\ln\left(\frac{1+x}{1-x}\right)\frac{\ln x}{1-x^2}\,dx\stackrel?=\frac{\pi^2}{24}\,\ln\left(\frac{A^{36}}{16\,\pi^3}\right)$

Published on 20 Dec 2015 - 22:14

score 1k · Answer 7 · 2015-12-21 20:21:14

1k

Views

Closed form for $\sum_{n=0}^\infty\frac{\Gamma\left(n+\tfrac14\right)}{2^n\,(4n+1)^2\,n!}$

Published on 21 Dec 2015 - 20:21

score 460 · Answer 8 · 2015-12-30 23:01:09

460

Views

Relationship between primes and practical numbers

Published on 30 Dec 2015 - 23:01

score 1.6k · Answer 9 · 2016-01-10 21:01:37

1.6k

Views

Conjecture ${\large\int}_0^\infty\left[\frac1{x^4}-\frac1{2x^3}+\frac1{12\,x^2}-\frac1{\left(e^x-1\right)x^3}\right]dx=\frac{\zeta(3)}{8\pi^2}$

Published on 10 Jan 2016 - 21:01

score 953 · Answer 10 · 2026-03-19 16:55:31

953

Views

Most wanted reproducible results in computational algebra

Published on 19 Mar 2026 - 16:55

score 39 · Answer 11 · 2016-01-27 03:24:07

39

Views

How to calculate these particular values in this experiment?

Published on 27 Jan 2016 - 3:24

score 201 · Answer 12 · 2016-02-13 16:11:12

201

Views

What subfields use computers the most and least? (soft question)

Published on 13 Feb 2016 - 16:11

score 49 · Answer 13 · 2016-02-25 06:50:05

49

Views

Method to study obvious properties

Published on 25 Feb 2016 - 6:50

score 63 · Answer 14 · 2016-02-29 11:23:59

63

Views

A computational experiment about identities involving the sum of remainders function

Published on 29 Feb 2016 - 11:23

score 37 · Answer 15 · 2016-04-18 08:42:03

37

Views

Assigning levels in factorial design.

Published on 18 Apr 2016 - 8:42

List Question

With $s(n)=\sum_{k=1}^n n \bmod k$, can be justified that $\forall\epsilon>0$ let us $\lim_{n\to\infty}\frac{s(n-1)}{\epsilon+s(n)}=1?$

Hints to compute if exists $\lim_{n\to\infty}\sum_{k=1}^n\sigma(k^2)/\sum_{k=1}^n\sigma(k)$, which $\sigma(n)=\sum_{d\mid n}d$, and other question

Please, help to identify this numerical constant

Trilogarithm $\operatorname{Li}_3(z)$ and the imaginary golden ratio $i\,\phi$

For $n\geq 1$, $\sum_{k=0}^{\infty}\frac{(-1)^{k}(nk+1)^{3}}{(k+1)^6}$ in terms of $\zeta(3)$ and $\zeta(5)$ from a series calculator. Is possible?

Conjecture $\int_0^1\ln\ln\left(\frac{1+x}{1-x}\right)\frac{\ln x}{1-x^2}\,dx\stackrel?=\frac{\pi^2}{24}\,\ln\left(\frac{A^{36}}{16\,\pi^3}\right)$

Closed form for $\sum_{n=0}^\infty\frac{\Gamma\left(n+\tfrac14\right)}{2^n\,(4n+1)^2\,n!}$

Relationship between primes and practical numbers

Conjecture ${\large\int}_0^\infty\left[\frac1{x^4}-\frac1{2x^3}+\frac1{12\,x^2}-\frac1{\left(e^x-1\right)x^3}\right]dx=\frac{\zeta(3)}{8\pi^2}$

Most wanted reproducible results in computational algebra

How to calculate these particular values in this experiment?

What subfields use computers the most and least? (soft question)

Method to study obvious properties

A computational experiment about identities involving the sum of remainders function

Assigning levels in factorial design.

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