Question

Identify sequences from OEIS or the literature, or find examples of odd integers $n\geq 1$ satisfying these equations related to odd perfect numbers

score 65 · Answer 1 · 2026-03-22 06:41:57

65

Views

Identify sequences from OEIS or the literature, or find examples of odd integers $n\geq 1$ satisfying these equations related to odd perfect numbers

Published on 22 Mar 2026 - 6:41

score 41 · Answer 2 · 2026-03-22 08:02:15

41

Views

Are there imperfects or pluperfects numbers?

Published on 22 Mar 2026 - 8:02

score 103 · Answer 3 · 2026-03-20 03:32:01

103

Views

If an odd perfect number exist could be a solitary number?

Published on 20 Mar 2026 - 3:32

score 271 · Answer 4 · 2026-03-19 20:52:48

271

Views

What about the equation $\sigma(2n)=2\left(n+\sigma(n)\right),$ involving the sum of divisor function?

Published on 19 Mar 2026 - 20:52

score 151 · Answer 5 · 2026-03-20 03:19:20

151

Views

Does the existence of infinite number of Leinster groups indicate the existence of infinite number of perfect numbers?

Published on 20 Mar 2026 - 3:19

score 113 · Answer 6 · 2026-03-20 08:20:28

113

Views

Bounds for an expression involving the divisors of an odd perfect number

Published on 20 Mar 2026 - 8:20

score 135 · Answer 7 · 2026-03-23 19:33:09

135

Views

Is there a $31$-dimensional manifold with 496 differential structures?

Published on 23 Mar 2026 - 19:33

score 142 · Answer 8 · 2026-03-22 03:11:04

142

Views

Is the occurence of two perfect numbers a coincidence?

Published on 22 Mar 2026 - 3:11

score 102 · Answer 9 · 2026-03-20 06:21:49

102

Views

If $q^k n^2$ is an odd perfect number with Euler prime $q$, does this equation imply that $k=1$?

Published on 20 Mar 2026 - 6:21

score 102 · Answer 10 · 2026-03-20 02:59:17

102

Views

On miscellaneous questions about perfect numbers III

Published on 20 Mar 2026 - 2:59

score 234 · Answer 11 · 2026-03-20 02:48:53

234

Views

Any proof for :Sum of two perfect number never be a perfect number?

Published on 20 Mar 2026 - 2:48

score 173 · Answer 12 · 2026-03-17 04:51:55

173

Views

Even perfect number that is also a sum of two cubes

Published on 17 Mar 2026 - 4:51

score 43 · Answer 13 · 2026-03-25 01:20:19

43

Views

Does there exist a natural number $N = xy$ satisfying $D(x)D(y) = 2s(x)s(y)$ with $\gcd(x,y)=1$?

Published on 25 Mar 2026 - 1:20

score 358 · Answer 14 · 2026-03-25 11:57:42

358

Views

If $\sigma(n)=2n$, how about the relationship between $\sigma(mn)$ and $2mn$?

Published on 25 Mar 2026 - 11:57

score 394 · Answer 15 · 2026-03-25 10:25:46

394

Views

If $n = km$ is a Descartes number with quasi-Euler prime $m$, then $m < k$.

Published on 25 Mar 2026 - 10:25

List Question

Identify sequences from OEIS or the literature, or find examples of odd integers $n\geq 1$ satisfying these equations related to odd perfect numbers

Are there imperfects or pluperfects numbers?

If an odd perfect number exist could be a solitary number?

What about the equation $\sigma(2n)=2\left(n+\sigma(n)\right),$ involving the sum of divisor function?

Does the existence of infinite number of Leinster groups indicate the existence of infinite number of perfect numbers?

Bounds for an expression involving the divisors of an odd perfect number

Is there a $31$-dimensional manifold with 496 differential structures?

Is the occurence of two perfect numbers a coincidence?

If $q^k n^2$ is an odd perfect number with Euler prime $q$, does this equation imply that $k=1$?

On miscellaneous questions about perfect numbers III

Any proof for :Sum of two perfect number never be a perfect number?

Even perfect number that is also a sum of two cubes

Does there exist a natural number $N = xy$ satisfying $D(x)D(y) = 2s(x)s(y)$ with $\gcd(x,y)=1$?

If $\sigma(n)=2n$, how about the relationship between $\sigma(mn)$ and $2mn$?

If $n = km$ is a Descartes number with quasi-Euler prime $m$, then $m < k$.

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