Question

If $N=q^k n^2$ is an odd perfect number, which is bigger, $\sigma(n^2)/n^2$ or $\sigma(n)/q^k$?

score 44 · Answer 1 · 2017-06-02 11:01:35

44

Views

If $N=q^k n^2$ is an odd perfect number, which is bigger, $\sigma(n^2)/n^2$ or $\sigma(n)/q^k$?

Published on 02 Jun 2017 - 11:01

score 52 · Answer 2 · 2017-06-02 14:51:57

52

Views

Building on work from previous MSE question 2306650 (Re: Odd Perfect Numbers)

Published on 02 Jun 2017 - 14:51

score 263 · Answer 3 · 2017-06-04 21:14:02

263

Views

Show that even perfect numbers (other than 6) have a remainder 1 on division by 9

Published on 04 Jun 2017 - 21:14

score 126 · Answer 4 · 2017-06-11 09:35:19

126

Views

A question on the Euler prime of odd perfect numbers

Published on 11 Jun 2017 - 9:35

score 95 · Answer 5 · 2017-06-23 15:53:48

95

Views

If $N=q^k n^2$ is an odd perfect number and $q = k$, why does this bound not imply $q > 5$?

Published on 23 Jun 2017 - 15:53

score 95 · Answer 6 · 2017-07-05 11:31:13

95

Views

Do all terms $n$ of OEIS sequence A228059 have a $p$ with exponent $1$?

Published on 05 Jul 2017 - 11:31

score 208 · Answer 7 · 2017-07-07 23:44:30

208

Views

Special prime of odd perfect number

Published on 07 Jul 2017 - 23:44

score 139 · Answer 8 · 2017-07-23 05:23:13

139

Views

Prove that $φ^x$ is close to an integer $y : x = 2^{n - 1}(2^n - 1)$

Published on 23 Jul 2017 - 5:23

score 144 · Answer 9 · 2017-07-24 17:51:33

144

Views

On the Descartes-Frenicle-Sorli conjecture and the Euler prime of odd perfect numbers

Published on 24 Jul 2017 - 17:51

score 160 · Answer 10 · 2017-08-03 11:12:29

160

Views

Show $n$ is perfect $\iff \sum\limits_{k=1}^{n-2}k\left\lfloor\frac{n}k\right\rfloor=1+\sum\limits_{k=1}^{n-1}k\left\lfloor\frac{n-1}k\right\rfloor$

Published on 03 Aug 2017 - 11:12

score 41 · Answer 11 · 2017-08-26 18:23:18

41

Views

If $q^k n^2$ is an odd perfect number with Euler prime $q$, does $\sigma(n^2)/q^k < q$ hold?

Published on 26 Aug 2017 - 18:23

score 532 · Answer 12 · 2017-09-04 13:36:25

532

Views

Odd Perfect number does not exist

Published on 04 Sep 2017 - 13:36

score 103 · Answer 13 · 2017-09-07 15:30:49

103

Views

If $q^k n^2$ is an odd perfect number with Euler prime $q$, which of the following relationships between $q^2$ and $n$ hold?

Published on 07 Sep 2017 - 15:30

score 102 · Answer 14 · 2017-09-18 06:02:11

Does $P = \big\{(2^n - 1)^2 - \sum_{k = 1}^{2^{n - 1} - 1}(4k - 1) : P = 2^{n - 1}(2^n - 1) = \text{Perfect Number}\big\}?$

score 1.4k · Answer 15 · 2017-09-22 20:58:06

1.4k

Views

"I am sure there are infinitely many perfect numbers"

Published on 22 Sep 2017 - 20:58

List Question

If $N=q^k n^2$ is an odd perfect number, which is bigger, $\sigma(n^2)/n^2$ or $\sigma(n)/q^k$?

Building on work from previous MSE question 2306650 (Re: Odd Perfect Numbers)

Show that even perfect numbers (other than 6) have a remainder 1 on division by 9

A question on the Euler prime of odd perfect numbers

If $N=q^k n^2$ is an odd perfect number and $q = k$, why does this bound not imply $q > 5$?

Do all terms $n$ of OEIS sequence A228059 have a $p$ with exponent $1$?

Special prime of odd perfect number

Prove that $φ^x$ is close to an integer $y : x = 2^{n - 1}(2^n - 1)$

On the Descartes-Frenicle-Sorli conjecture and the Euler prime of odd perfect numbers

Show $n$ is perfect $\iff \sum\limits_{k=1}^{n-2}k\left\lfloor\frac{n}k\right\rfloor=1+\sum\limits_{k=1}^{n-1}k\left\lfloor\frac{n-1}k\right\rfloor$

If $q^k n^2$ is an odd perfect number with Euler prime $q$, does $\sigma(n^2)/q^k < q$ hold?

Odd Perfect number does not exist

If $q^k n^2$ is an odd perfect number with Euler prime $q$, which of the following relationships between $q^2$ and $n$ hold?

Does $P = \big\{(2^n - 1)^2 - \sum_{k = 1}^{2^{n - 1} - 1}(4k - 1) : P = 2^{n - 1}(2^n - 1) = \text{Perfect Number}\big\}?$

"I am sure there are infinitely many perfect numbers"

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