Question

Weighted Sum of Divisor Function For the first N Natural Numbers

score 89 · Answer 1 · 2026-03-26 11:00:16

89

Views

Weighted Sum of Divisor Function For the first N Natural Numbers

Published on 26 Mar 2026 - 11:00

score 1.1k · Answer 2 · 2010-11-06 12:42:24

1.1k

Views

Proving $ \frac{\sigma(n)}{n} < \frac{n}{\varphi(n)} < \frac{\pi^{2}}{6} \frac{\sigma(n)}{n}$

Published on 06 Nov 2010 - 12:42

score 187 · Answer 3 · 2011-08-16 17:51:40

187

Views

$\sum_{i=1}^n |\{k \in \mathbb{N} \mid k | i\}|$

Published on 16 Aug 2011 - 17:51

score 709 · Answer 4 · 2011-12-30 04:43:34

709

Views

Sum of divisor ratio inequality

Published on 30 Dec 2011 - 4:43

score 1.1k · Answer 5 · 2012-02-06 22:16:25

1.1k

Views

An approximate relationship between the totient function and sum of divisors

Published on 06 Feb 2012 - 22:16

score 142 · Answer 6 · 2012-02-09 15:26:22

142

Views

Composite $n$ such that $\sigma(n) \equiv n+1 \pmod{\phi(n)}$

Published on 09 Feb 2012 - 15:26

score 2.5k · Answer 7 · 2026-03-26 12:53:31

2.5k

Views

Sum of Positive Divisors: $\sum_{d|n} \mu(n/d)\nu(d)=1$ and $\sum_{d|n} \mu(n/d)\sigma(d)=n$

Published on 26 Mar 2026 - 12:53

score 7.6k · Answer 8 · 2012-06-12 15:52:07

7.6k

Views

Show that $\sum\nolimits_{d|n} \frac{1}{d} = \frac{\sigma (n)}{n}$ for every positive integer $n$.

Published on 12 Jun 2012 - 15:52

score 2.6k · Answer 9 · 2012-08-25 06:43:00

2.6k

Views

When is the sum of divisors a prime?

Published on 25 Aug 2012 - 6:43

score 399 · Answer 10 · 2012-09-23 15:42:38

399

Views

Inclusion Exclusion and lcm

Published on 23 Sep 2012 - 15:42

score 204 · Answer 11 · 2013-02-14 21:12:07

204

Views

Finding $\frac{1}{d_1}+\frac{1}{d_2}+\frac{1}{d_3}+...+\frac{1}{d_k}$

Published on 14 Feb 2013 - 21:12

score 790 · Answer 12 · 2020-07-31 16:42:24

790

Views

USA TST 2018/P1: Prove that the $n^{\text{th}}$ smallest positive integer relatively prime to $n$ is at least $\sigma(n)$

Published on 31 Jul 2020 - 16:42

score 35 · Answer 13 · 2026-03-28 10:41:27

35

Views

Bounds for $\frac{\sigma(q^k)}{2\sigma(q^{k-1})}$ in terms of $q$ and $k$

Published on 28 Mar 2026 - 10:41

score 146 · Answer 14 · 2026-03-27 08:46:39

146

Views

Is this a valid proof for $I(n^2) \geq \frac{5}{3}$, if $q^k n^2$ is an odd perfect number with special prime $q$?

Published on 27 Mar 2026 - 8:46

score 523 · Answer 15 · 2026-03-28 10:35:25

523

Views

Does the equation $\sigma(\sigma(x^2))=2x\sigma(x)$ have any odd solutions?

Published on 28 Mar 2026 - 10:35

List Question

Weighted Sum of Divisor Function For the first N Natural Numbers

Proving $ \frac{\sigma(n)}{n} < \frac{n}{\varphi(n)} < \frac{\pi^{2}}{6} \frac{\sigma(n)}{n}$

$\sum_{i=1}^n |\{k \in \mathbb{N} \mid k | i\}|$

Sum of divisor ratio inequality

An approximate relationship between the totient function and sum of divisors

Composite $n$ such that $\sigma(n) \equiv n+1 \pmod{\phi(n)}$

Sum of Positive Divisors: $\sum_{d|n} \mu(n/d)\nu(d)=1$ and $\sum_{d|n} \mu(n/d)\sigma(d)=n$

Show that $\sum\nolimits_{d|n} \frac{1}{d} = \frac{\sigma (n)}{n}$ for every positive integer $n$.

When is the sum of divisors a prime?

Inclusion Exclusion and lcm

Finding $\frac{1}{d_1}+\frac{1}{d_2}+\frac{1}{d_3}+...+\frac{1}{d_k}$

USA TST 2018/P1: Prove that the $n^{\text{th}}$ smallest positive integer relatively prime to $n$ is at least $\sigma(n)$

Bounds for $\frac{\sigma(q^k)}{2\sigma(q^{k-1})}$ in terms of $q$ and $k$

Is this a valid proof for $I(n^2) \geq \frac{5}{3}$, if $q^k n^2$ is an odd perfect number with special prime $q$?

Does the equation $\sigma(\sigma(x^2))=2x\sigma(x)$ have any odd solutions?

Trending Questions

Popular # Hahtags

Popular Questions