Question

On the quantity $I(q^k) + I(n^2)$ considered as functions of $q$ and $k$, when $q^k n^2$ is an odd perfect number with special prime $q$

score 70 · Answer 1 · 2021-04-16 12:28:33

70

Views

On the quantity $I(q^k) + I(n^2)$ considered as functions of $q$ and $k$, when $q^k n^2$ is an odd perfect number with special prime $q$

Published on 16 Apr 2021 - 12:28

score 182 · Answer 2 · 2021-05-06 05:22:45

182

Views

Book recommendation/reference request on a gentle introduction to cyclotomic polynomials

Published on 06 May 2021 - 5:22

score 66 · Answer 3 · 2021-05-09 08:10:28

66

Views

Follow-up to question 3121498, asked in February 2019

Published on 09 May 2021 - 8:10

score 123 · Answer 4 · 2021-05-12 09:20:12

123

Views

If $p^k m^2$ is an odd perfect number, then is there a constant $D$ such that $\frac{\sigma(m^2)}{p^k} > \frac{m^2 - p^k}{D}$?

Published on 12 May 2021 - 9:20

score 226 · Answer 5 · 2021-06-01 05:26:33

226

Views

On odd perfect numbers $p^k m^2$ with special prime $p$, satisfying $m^2 - p^k = 2^r t$

Published on 01 Jun 2021 - 5:26

score 133 · Answer 6 · 2021-06-04 03:50:03

133

Views

If $p^k m^2$ is an odd perfect number with special prime $p$, then which is larger: $D(p^k)$ or $D(m^2)$?

Published on 04 Jun 2021 - 3:50

score 231 · Answer 7 · 2021-06-08 00:05:03

231

Views

odd perfect numbers mod $9$

Published on 08 Jun 2021 - 0:05

score 118 · Answer 8 · 2021-06-11 04:07:53

118

Views

On an inequality involving the abundancy index of the Eulerian component $p^k$ of an odd perfect number $p^k m^2$

Published on 11 Jun 2021 - 4:07

score 422 · Answer 9 · 2021-06-12 05:19:30

422

Views

On odd perfect numbers $p^k m^2$ with special prime $p$ satisfying $m^2 - p^k = 2^r t$ - Part II

Published on 12 Jun 2021 - 5:19

score 99 · Answer 10 · 2021-06-18 14:18:51

99

Views

Sum of first $n$ perfect numbers

Published on 18 Jun 2021 - 14:18

score 97 · Answer 11 · 2021-06-28 11:45:57

97

Views

Improving $\dfrac{120}{217\zeta(3)} < \dfrac{\varphi(m)}{m}$ to $\dfrac{1}{2} < \dfrac{\varphi(m)}{m}$, where $p^k m^2$ is an odd perfect number

Published on 28 Jun 2021 - 11:45

score 49 · Answer 12 · 2021-07-03 22:01:29

49

Views

Improving $I(m) < 2$, if $p^k m^2$ is an odd perfect number with special prime $p$

Published on 03 Jul 2021 - 22:01

score 217 · Answer 13 · 2021-07-04 10:16:48

217

Views

If $p^k m^2$ is an odd perfect number with special prime $p$, then which is larger: $D(p^k)$ or $D(m)$?

Published on 04 Jul 2021 - 10:16

score 36 · Answer 14 · 2021-07-06 06:41:04

36

Views

Does this "improvement" to $I(m) < 2$, if $p^k m^2$ is an odd perfect number with special prime $p$, work?

Published on 06 Jul 2021 - 6:41

score 137 · Answer 15 · 2021-07-07 03:49:49

137

Views

On P. Starni's "Some Extensions to Touchard's Theorem on Odd Perfect Numbers"

Published on 07 Jul 2021 - 3:49

List Question

On the quantity $I(q^k) + I(n^2)$ considered as functions of $q$ and $k$, when $q^k n^2$ is an odd perfect number with special prime $q$

Book recommendation/reference request on a gentle introduction to cyclotomic polynomials

Follow-up to question 3121498, asked in February 2019

If $p^k m^2$ is an odd perfect number, then is there a constant $D$ such that $\frac{\sigma(m^2)}{p^k} > \frac{m^2 - p^k}{D}$?

On odd perfect numbers $p^k m^2$ with special prime $p$, satisfying $m^2 - p^k = 2^r t$

If $p^k m^2$ is an odd perfect number with special prime $p$, then which is larger: $D(p^k)$ or $D(m^2)$?

odd perfect numbers mod $9$

On an inequality involving the abundancy index of the Eulerian component $p^k$ of an odd perfect number $p^k m^2$

On odd perfect numbers $p^k m^2$ with special prime $p$ satisfying $m^2 - p^k = 2^r t$ - Part II

Sum of first $n$ perfect numbers

Improving $\dfrac{120}{217\zeta(3)} < \dfrac{\varphi(m)}{m}$ to $\dfrac{1}{2} < \dfrac{\varphi(m)}{m}$, where $p^k m^2$ is an odd perfect number

Improving $I(m) < 2$, if $p^k m^2$ is an odd perfect number with special prime $p$

If $p^k m^2$ is an odd perfect number with special prime $p$, then which is larger: $D(p^k)$ or $D(m)$?

Does this "improvement" to $I(m) < 2$, if $p^k m^2$ is an odd perfect number with special prime $p$, work?

On P. Starni's "Some Extensions to Touchard's Theorem on Odd Perfect Numbers"

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