Question

Does the following lower bound improve on $I(q^k) + I(n^2) > 3 - \frac{q-2}{q(q-1)}$, where $q^k n^2$ is an odd perfect number? - Part II

score 519 · Answer 1 · 2021-07-13 09:17:05

519

Views

Does the following lower bound improve on $I(q^k) + I(n^2) > 3 - \frac{q-2}{q(q-1)}$, where $q^k n^2$ is an odd perfect number? - Part II

Published on 13 Jul 2021 - 9:17

score 112 · Answer 2 · 2021-07-13 13:13:42

112

Views

Does $\sigma(n^2)/q \mid q^k n^2$ imply $\sigma(n^2)/q \mid n^2$, if $q^k n^2$ is an odd perfect number with special prime $q$?

Published on 13 Jul 2021 - 13:13

score 76 · Answer 3 · 2021-07-14 12:15:23

76

Views

On the sum $I(q^k) + I(n^2)$, where $q^k n^2$ is an odd perfect number with special prime $q$

Published on 14 Jul 2021 - 12:15

score 70 · Answer 4 · 2021-07-15 11:02:22

70

Views

On the equation $\frac{1}{q}=1-\frac{\varphi(N)/N}{\varphi(n)/n}$, where $N=q^k n^2$ is an odd perfect number with special prime $q$

Published on 15 Jul 2021 - 11:02

score 128 · Answer 5 · 2021-07-30 09:53:25

128

Views

Is it true that $\frac{D(n^2)}{s(q^k)} > \frac{\sigma(q^k)}{2}$, if $q^k n^2$ is an odd perfect number given in Eulerian form?

Published on 30 Jul 2021 - 9:53

score 166 · Answer 6 · 2021-07-31 05:17:03

166

Views

Is this proof regarding the nonexistence of odd perfect numbers correct?

Published on 31 Jul 2021 - 5:17

score 497 · Answer 7 · 2021-08-04 10:00:27

497

Views

Proof-verification request: If $q^k n^2$ is an odd perfect number with special prime $q$, then $q < n^{2/5}$.

Published on 04 Aug 2021 - 10:00

score 113 · Answer 8 · 2021-08-13 06:39:51

113

Views

If $N = q^k n^2$ is an odd perfect number with special prime $q$, then must $\sigma(n^2)$ be abundant?

Published on 13 Aug 2021 - 6:39

score 65 · Answer 9 · 2021-08-23 08:42:44

65

Views

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

Published on 23 Aug 2021 - 8:42

score 115 · Answer 10 · 2021-09-05 07:20:36

115

Views

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

Published on 05 Sep 2021 - 7:20

score 206 · Answer 11 · 2021-09-08 16:30:59

206

Views

If an odd perfect number exists, does it have exactly one prime factor of the form $4a+1$?

Published on 08 Sep 2021 - 16:30

score 118 · Answer 12 · 2021-09-12 08:18:51

118

Views

On the inequality $I(n^2) \geq (6 - s(q^k))/3$, where $q^k n^2$ is an odd perfect number and $I(x)$ is the abundancy index of $x$

Published on 12 Sep 2021 - 8:18

score 82 · Answer 13 · 2021-09-17 08:42:34

82

Views

How do number shapes relate to k-perfect numbers?

Published on 17 Sep 2021 - 8:42

score 121 · Answer 14 · 2021-09-20 05:10:37

121

Views

How to find all even perfect number of a particular form.

Published on 20 Sep 2021 - 5:10

score 172 · Answer 15 · 2021-09-25 06:59:04

172

Views

On odd perfect numbers and a GCD - Part IV

Published on 25 Sep 2021 - 6:59

List Question

Does the following lower bound improve on $I(q^k) + I(n^2) > 3 - \frac{q-2}{q(q-1)}$, where $q^k n^2$ is an odd perfect number? - Part II

Does $\sigma(n^2)/q \mid q^k n^2$ imply $\sigma(n^2)/q \mid n^2$, if $q^k n^2$ is an odd perfect number with special prime $q$?

On the sum $I(q^k) + I(n^2)$, where $q^k n^2$ is an odd perfect number with special prime $q$

On the equation $\frac{1}{q}=1-\frac{\varphi(N)/N}{\varphi(n)/n}$, where $N=q^k n^2$ is an odd perfect number with special prime $q$

Is it true that $\frac{D(n^2)}{s(q^k)} > \frac{\sigma(q^k)}{2}$, if $q^k n^2$ is an odd perfect number given in Eulerian form?

Is this proof regarding the nonexistence of odd perfect numbers correct?

Proof-verification request: If $q^k n^2$ is an odd perfect number with special prime $q$, then $q < n^{2/5}$.

If $N = q^k n^2$ is an odd perfect number with special prime $q$, then must $\sigma(n^2)$ be abundant?

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

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

If an odd perfect number exists, does it have exactly one prime factor of the form $4a+1$?

On the inequality $I(n^2) \geq (6 - s(q^k))/3$, where $q^k n^2$ is an odd perfect number and $I(x)$ is the abundancy index of $x$

How do number shapes relate to k-perfect numbers?

How to find all even perfect number of a particular form.

On odd perfect numbers and a GCD - Part IV

Trending Questions

Popular # Hahtags

Popular Questions