Question

$\sum_{p\leq n}\sum_{q\leq N}\sum_{n\leq N;p|n,q|n}1=^? \sum_{pq \leq N}\big( \frac N{pq}+O(1)\big)+\sum_{p \leq N}\big( \frac N{p}-\frac N{p^2}\big)$

score 105 · Answer 1 · 2018-02-20 18:14:44

105

Views

$\sum_{p\leq n}\sum_{q\leq N}\sum_{n\leq N;p|n,q|n}1=^? \sum_{pq \leq N}\big( \frac N{pq}+O(1)\big)+\sum_{p \leq N}\big( \frac N{p}-\frac N{p^2}\big)$

Published on 20 Feb 2018 - 18:14

score 225 · Answer 2 · 2026-03-22 14:40:38

225

Views

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

Published on 22 Mar 2026 - 14:40

score 271 · Answer 3 · 2018-02-21 13:18:28

271

Views

$\sum_{k=1}^n\frac{1}{\sin^2\left(\frac{(2k+1)\pi}{2n}\right)}$

Published on 21 Feb 2018 - 13:18

score 199 · Answer 4 · 2018-02-21 14:07:31

199

Views

Changing the index of a summation for probability density functions

Published on 21 Feb 2018 - 14:07

score 74 · Answer 5 · 2026-03-25 14:26:03

74

Views

Calculate the sum $ \sum\limits_{i=1}^n \sum\limits_{j=1}^n a_i \mod a_j $ in $\mathbb{Z}.$

Published on 25 Mar 2026 - 14:26

score 347 · Answer 6 · 2026-03-25 12:34:32

347

Views

Can we write $\ln(x) $ as an infinite sum of $n$ th roots?

Published on 25 Mar 2026 - 12:34

score 120 · Answer 7 · 2026-03-25 12:35:05

120

Views

Justify an approximation of $\sum_{n=1}^\infty G_n\zeta(n+1)$, where $G_m$ denotes the so-called Gregory coefficients

Published on 25 Mar 2026 - 12:35

score 148 · Answer 8 · 2018-02-21 20:17:37

148

Views

Summation that gets smaller with greater index

Published on 21 Feb 2018 - 20:17

score 53 · Answer 9 · 2018-02-22 02:28:26

53

Views

Does there always exist real numbers $w_{1},\dots, w_{n} > 0$ of such a kind?

Published on 22 Feb 2018 - 2:28

score 72 · Answer 10 · 2018-02-22 02:48:36

72

Views

Finding the sum of $\sum_{i=0}^{2n} (-2)^i$

Published on 22 Feb 2018 - 2:48

score 84 · Answer 11 · 2026-03-25 09:24:16

84

Views

Variance of the sum of complex random variable

Published on 25 Mar 2026 - 9:24

score 75 · Answer 12 · 2018-02-22 17:00:37

75

Views

Show that this equation is equal to $\sum_{k=2}^{2n+1}\frac{2}{k^2-1}$

Published on 22 Feb 2018 - 17:00

score 3.4k · Answer 13 · 2026-03-25 01:18:36

3.4k

Views

How to simplify sum of $x_i Y_i$. where the sum of $x_i$ is a constant?

Published on 25 Mar 2026 - 1:18

score 98 · Answer 14 · 2026-03-25 12:31:23

98

Views

What is time complexity of my algorithm

Published on 25 Mar 2026 - 12:31

score 258 · Answer 15 · 2026-03-25 11:08:27

258

Views

Finite Binomial Sum

Published on 25 Mar 2026 - 11:08

List Question

$\sum_{p\leq n}\sum_{q\leq N}\sum_{n\leq N;p|n,q|n}1=^? \sum_{pq \leq N}\big( \frac N{pq}+O(1)\big)+\sum_{p \leq N}\big( \frac N{p}-\frac N{p^2}\big)$

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

$\sum_{k=1}^n\frac{1}{\sin^2\left(\frac{(2k+1)\pi}{2n}\right)}$

Changing the index of a summation for probability density functions

Calculate the sum $ \sum\limits_{i=1}^n \sum\limits_{j=1}^n a_i \mod a_j $ in $\mathbb{Z}.$

Can we write $\ln(x) $ as an infinite sum of $n$ th roots?

Justify an approximation of $\sum_{n=1}^\infty G_n\zeta(n+1)$, where $G_m$ denotes the so-called Gregory coefficients

Summation that gets smaller with greater index

Does there always exist real numbers $w_{1},\dots, w_{n} > 0$ of such a kind?

Finding the sum of $\sum_{i=0}^{2n} (-2)^i$

Variance of the sum of complex random variable

Show that this equation is equal to $\sum_{k=2}^{2n+1}\frac{2}{k^2-1}$

How to simplify sum of $x_i Y_i$. where the sum of $x_i$ is a constant?

What is time complexity of my algorithm

Finite Binomial Sum

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