Question

Can $\sigma(n)-n$ be a proper divisor of $n$?

score 135 · Answer 1 · 2015-06-19 12:11:00

135

Views

Can $\sigma(n)-n$ be a proper divisor of $n$?

Published on 19 Jun 2015 - 12:11

score 127 · Answer 2 · 2015-06-22 06:17:09

127

Views

Solve the equation $\sigma{(n)}=n$

Published on 22 Jun 2015 - 6:17

score 511 · Answer 3 · 2015-07-04 07:04:22

511

Views

$n^2(n-1)\sigma(n)=0 \mod 12$, where $\sigma(n)$ is the sum of divisors function

Published on 04 Jul 2015 - 7:04

score 264 · Answer 4 · 2026-03-25 22:05:02

264

Views

How do I prove that there is no other :$k=9,12,18$ for which this fails :$\sigma^k(114) \equiv 0\mod 6 $?

Published on 25 Mar 2026 - 22:05

score 321 · Answer 5 · 2015-07-12 23:29:26

321

Views

Is the integer $0$ a deficient number?

Published on 12 Jul 2015 - 23:29

score 467 · Answer 6 · 2015-07-15 16:21:22

467

Views

Sum of factors of multiplication of different numbers

Published on 15 Jul 2015 - 16:21

score 311 · Answer 7 · 2015-07-16 18:02:39

311

Views

Is it possible to determine the number divisors of n! especially for large n?

Published on 16 Jul 2015 - 18:02

score 87 · Answer 8 · 2026-03-26 18:40:58

87

Views

How do I show $1$ is not a trivial odd perfect number?

Published on 26 Mar 2026 - 18:40

score 101 · Answer 9 · 2015-07-18 07:32:19

101

Views

Sum involving the Möbius function

Published on 18 Jul 2015 - 7:32

score 415 · Answer 10 · 2026-03-26 18:40:54

415

Views

When does :$\sigma(\sigma(2n))=\sigma(\sigma(n))$ and $\sigma(n)$ is sum divisors of the positive integer $n$?

Published on 26 Mar 2026 - 18:40

score 209 · Answer 11 · 2015-07-19 01:52:11

209

Views

How do I show that :$\sigma({p^m})$ is divisible by $4$ if $m=4k+1$ , and $k$ is an integer number?

Published on 19 Jul 2015 - 1:52

score 345 · Answer 12 · 2026-03-26 06:11:01

345

Views

Is this : $\lim \sup\frac{\sigma(n)}{n} , n \to\infty $ has a finite limit?

Published on 26 Mar 2026 - 6:11

score 76 · Answer 13 · 2015-07-22 02:31:45

76

Views

Is this :$\sum_{n=1}^{\infty} \frac{\sigma_{k}(n)}{n!} $ irrational series for every natural number $k$?

Published on 22 Jul 2015 - 2:31

score 45 · Answer 14 · 2015-07-30 14:57:07

45

Views

Are there infinitely many $k$ for which $\frac{\sigma(k)}{k}$ is a rational square where $ \sigma(k) $ and $k$ both are square?

Published on 30 Jul 2015 - 14:57

score 144 · Answer 15 · 2026-03-25 19:51:28

144

Views

If $\varphi(mn)=\lambda \varphi(m)\varphi(n)$ what should be written for $\lambda$

Published on 25 Mar 2026 - 19:51

List Question

Can $\sigma(n)-n$ be a proper divisor of $n$?

Solve the equation $\sigma{(n)}=n$

$n^2(n-1)\sigma(n)=0 \mod 12$, where $\sigma(n)$ is the sum of divisors function

How do I prove that there is no other :$k=9,12,18$ for which this fails :$\sigma^k(114) \equiv 0\mod 6 $?

Is the integer $0$ a deficient number?

Sum of factors of multiplication of different numbers

Is it possible to determine the number divisors of n! especially for large n?

How do I show $1$ is not a trivial odd perfect number?

Sum involving the Möbius function

When does :$\sigma(\sigma(2n))=\sigma(\sigma(n))$ and $\sigma(n)$ is sum divisors of the positive integer $n$?

How do I show that :$\sigma({p^m})$ is divisible by $4$ if $m=4k+1$ , and $k$ is an integer number?

Is this : $\lim \sup\frac{\sigma(n)}{n} , n \to\infty $ has a finite limit?

Is this :$\sum_{n=1}^{\infty} \frac{\sigma_{k}(n)}{n!} $ irrational series for every natural number $k$?

Are there infinitely many $k$ for which $\frac{\sigma(k)}{k}$ is a rational square where $ \sigma(k) $ and $k$ both are square?

If $\varphi(mn)=\lambda \varphi(m)\varphi(n)$ what should be written for $\lambda$

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