Question

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

score 300 · Answer 1 · 2020-09-18 10:46:01

300

Views

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

Published on 18 Sep 2020 - 10:46

score 53 · Answer 2 · 2020-09-19 06:32:49

53

Views

Books/monographs/handouts specifically about perfect numbers and related topics

Published on 19 Sep 2020 - 6:32

score 134 · Answer 3 · 2020-09-23 02:54:36

134

Views

A Question Pertaining to Benjamin Peirce and Odd Perfect Numbers

Published on 23 Sep 2020 - 2:54

score 525 · Answer 4 · 2020-09-25 07:12:08

525

Views

Van der Pol's identity for the sum of divisors and a quartic polynomial equation for odd perfect numbers

Published on 25 Sep 2020 - 7:12

score 196 · Answer 5 · 2020-10-07 08:26:12

196

Views

A geometric approach to the odd perfect number problem?

Published on 07 Oct 2020 - 8:26

score 127 · Answer 6 · 2020-10-14 11:22:14

127

Views

On odd perfect numbers $q^k n^2$ and the deficient-perfect divisor $q^{\frac{k-1}{2}} n^2$ - Part II

Published on 14 Oct 2020 - 11:22

score 107 · Answer 7 · 2020-10-16 04:09:56

107

Views

On the Second and Third Largest Prime Divisors of an Odd Perfect Number

Published on 16 Oct 2020 - 4:09

score 141 · Answer 8 · 2020-10-20 11:23:20

141

Views

Is this proof regarding odd perfect numbers valid?

Published on 20 Oct 2020 - 11:23

score 153 · Answer 9 · 2020-10-31 05:56:04

153

Views

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

Published on 31 Oct 2020 - 5:56

score 60 · Answer 10 · 2020-11-01 02:00:51

60

Views

Does $D_k \mid N_k$ hold at every step of this iterative process involving divisors of odd perfect numbers?

Published on 01 Nov 2020 - 2:00

score 258 · Answer 11 · 2020-11-11 10:18:25

258

Views

On the nearest-square function - Part 2 and the quantity $m^2 - p^k$ where $p^k m^2$ is an odd perfect number

Published on 11 Nov 2020 - 10:18

score 238 · Answer 12 · 2020-11-24 05:36:15

238

Views

If $p^k m^2$ is an odd perfect number, then what is the optimal constant $C$ such that $\frac{\sigma(m^2)}{p^k} < \frac{m^2 - p^k}{C}$?

Published on 24 Nov 2020 - 5:36

score 114 · Answer 13 · 2020-12-02 14:14:29

114

Views

On a curious equation regarding odd perfect numbers

Published on 02 Dec 2020 - 14:14

score 188 · Answer 14 · 2020-12-03 07:39:57

188

Views

Why does an odd perfect number seemingly "violate" basic inequality rules?

Published on 03 Dec 2020 - 7:39

score 126 · Answer 15 · 2020-12-13 01:51:42

126

Views

Is every multiperfect number also pseudoperfect?

Published on 13 Dec 2020 - 1:51

List Question

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

Books/monographs/handouts specifically about perfect numbers and related topics

A Question Pertaining to Benjamin Peirce and Odd Perfect Numbers

Van der Pol's identity for the sum of divisors and a quartic polynomial equation for odd perfect numbers

A geometric approach to the odd perfect number problem?

On odd perfect numbers $q^k n^2$ and the deficient-perfect divisor $q^{\frac{k-1}{2}} n^2$ - Part II

On the Second and Third Largest Prime Divisors of an Odd Perfect Number

Is this proof regarding odd perfect numbers valid?

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

Does $D_k \mid N_k$ hold at every step of this iterative process involving divisors of odd perfect numbers?

On the nearest-square function - Part 2 and the quantity $m^2 - p^k$ where $p^k m^2$ is an odd perfect number

If $p^k m^2$ is an odd perfect number, then what is the optimal constant $C$ such that $\frac{\sigma(m^2)}{p^k} < \frac{m^2 - p^k}{C}$?

On a curious equation regarding odd perfect numbers

Why does an odd perfect number seemingly "violate" basic inequality rules?

Is every multiperfect number also pseudoperfect?

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