Question

Any value $n$ we can conclude there are no perfect numbers of the form $kn+1$ or congruent to $1$ $\pmod n$?

score 104 · Answer 1 · 2016-11-11 00:50:23

104

Views

Any value $n$ we can conclude there are no perfect numbers of the form $kn+1$ or congruent to $1$ $\pmod n$?

Published on 11 Nov 2016 - 0:50

score 513 · Answer 2 · 2016-12-03 14:03:02

513

Views

If $n$ is an odd perfect number then $n=p_1^{j_1}p_2^{2j_2}...p_r^{2j_r}$ where $p_i$ are distinct odd primes and $p_1\equiv j_1 \equiv 1 \pmod 4.$

Published on 03 Dec 2016 - 14:03

score 139 · Answer 3 · 2016-12-12 22:49:57

139

Views

S-sets (even though this title is too short)

Published on 12 Dec 2016 - 22:49

score 369 · Answer 4 · 2016-12-21 11:02:42

369

Views

What is the asymptotic density of deficient-perfect numbers?

Published on 21 Dec 2016 - 11:02

score 214 · Answer 5 · 2016-12-29 16:09:49

214

Views

Assuming the Lenstra–Pomerance–Wagstaff conjecture, in what range of values for $p$ would we expect to find the next prime $2^p - 1$?

Published on 29 Dec 2016 - 16:09

score 160 · Answer 6 · 2017-01-02 11:30:57

160

Views

Can an odd perfect number be a nontrivial multiple of a triangular number?

Published on 02 Jan 2017 - 11:30

score 869 · Answer 7 · 2017-01-09 20:24:15

869

Views

When $p$ is an odd prime, is $(p+2)/p$ an outlaw or an index?

Published on 09 Jan 2017 - 20:24

score 82 · Answer 8 · 2017-01-09 20:35:48

82

Views

Does there exist an integer $m$ which is not in the image of $D(n)=2n - \sigma(n)$?

Published on 09 Jan 2017 - 20:35

score 547 · Answer 9 · 2017-01-17 21:57:04

547

Views

Perfect numbers adding up to 10

Published on 17 Jan 2017 - 21:57

score 116 · Answer 10 · 2017-01-18 10:12:24

116

Views

If $q^k n^2$ is an odd perfect number with Euler prime $q$, does $I(n^2) \geq 5/3$ imply $k=1$?

Published on 18 Jan 2017 - 10:12

score 245 · Answer 11 · 2017-01-18 19:39:51

245

Views

On odd perfect numbers $n$ and $\sigma\left(n^\lambda\right)$

Published on 18 Jan 2017 - 19:39

score 1k · Answer 12 · 2017-01-21 11:24:03

1k

Views

Perfect and factorial numbers

Published on 21 Jan 2017 - 11:24

score 150 · Answer 13 · 2017-01-23 07:54:01

150

Views

Are perfect numbers definable in $(\Bbb N, 0, 1, +, \cdot)$?

Published on 23 Jan 2017 - 7:54

score 182 · Answer 14 · 2017-01-24 18:14:36

182

Views

If $N = q^k n^2$ is an odd perfect number with $k > 1$ and $N = \frac{q(q+1)}{2} \cdot d$ for some $d > 1$, then what is $d$?

Published on 24 Jan 2017 - 18:14

score 246 · Answer 15 · 2017-01-24 19:41:12

246

Views

Is there a (conjectured) relationship between triangular numbers and friendly numbers?

Published on 24 Jan 2017 - 19:41

List Question

Any value $n$ we can conclude there are no perfect numbers of the form $kn+1$ or congruent to $1$ $\pmod n$?

If $n$ is an odd perfect number then $n=p_1^{j_1}p_2^{2j_2}...p_r^{2j_r}$ where $p_i$ are distinct odd primes and $p_1\equiv j_1 \equiv 1 \pmod 4.$

S-sets (even though this title is too short)

What is the asymptotic density of deficient-perfect numbers?

Assuming the Lenstra–Pomerance–Wagstaff conjecture, in what range of values for $p$ would we expect to find the next prime $2^p - 1$?

Can an odd perfect number be a nontrivial multiple of a triangular number?

When $p$ is an odd prime, is $(p+2)/p$ an outlaw or an index?

Does there exist an integer $m$ which is not in the image of $D(n)=2n - \sigma(n)$?

Perfect numbers adding up to 10

If $q^k n^2$ is an odd perfect number with Euler prime $q$, does $I(n^2) \geq 5/3$ imply $k=1$?

On odd perfect numbers $n$ and $\sigma\left(n^\lambda\right)$

Perfect and factorial numbers

Are perfect numbers definable in $(\Bbb N, 0, 1, +, \cdot)$?

If $N = q^k n^2$ is an odd perfect number with $k > 1$ and $N = \frac{q(q+1)}{2} \cdot d$ for some $d > 1$, then what is $d$?

Is there a (conjectured) relationship between triangular numbers and friendly numbers?

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