Question

Are there (restricted) instances when the deficiency and sum-of-proper-divisors functions are multiplicative?

score 82 · Answer 1 · 2026-03-25 11:07:01

82

Views

Are there (restricted) instances when the deficiency and sum-of-proper-divisors functions are multiplicative?

Published on 25 Mar 2026 - 11:07

score 35 · Answer 2 · 2026-03-25 14:22:31

35

Views

Does $2r - \sigma(r)$ divide $\sigma(r)$ if $r$ is deficient-perfect?

Published on 25 Mar 2026 - 14:22

score 46 · Answer 3 · 2026-03-25 17:21:48

46

Views

If $q^k n^2$ is an odd perfect number with special prime $q$, then does $(q+1)/2 \mid \sigma(n^2)$ hold?

Published on 25 Mar 2026 - 17:21

score 28 · Answer 4 · 2026-03-25 16:02:16

28

Views

Does $\gcd(r, \sigma(r)) = 2r - \sigma(r)$ always hold when $r$ is deficient-perfect?

Published on 25 Mar 2026 - 16:02

score 164 · Answer 5 · 2019-08-11 15:20:28

164

Views

What is wrong with my proof of there is no odd perfect number?

Published on 11 Aug 2019 - 15:20

score 55 · Answer 6 · 2026-03-25 14:21:41

55

Views

Question on Potential Relationship between Mertens Function and Perfect Number Counting Function

Published on 25 Mar 2026 - 14:21

score 103 · Answer 7 · 2026-03-25 11:03:38

103

Views

Conjecture That The Only Nearly Perfect Numbers Are The Powers Of 2

Published on 25 Mar 2026 - 11:03

score 102 · Answer 8 · 2026-03-25 14:25:20

102

Views

An interesting identity involving the abundancy index of divisors of odd perfect numbers

Published on 25 Mar 2026 - 14:25

score 115 · Answer 9 · 2026-03-25 11:16:04

115

Views

Are there any odd perfect numbers in base $g$, where $g \neq 10$?

Published on 25 Mar 2026 - 11:16

score 143 · Answer 10 · 2026-03-25 17:21:42

143

Views

Bounds for the abundancy index of divisors of odd perfect numbers in terms of the deficiency function

Published on 25 Mar 2026 - 17:21

score 448 · Answer 11 · 2014-03-14 09:14:45

448

Views

Perfect numbers and powers of two

Published on 14 Mar 2014 - 9:14

score 1.3k · Answer 12 · 2026-03-25 12:50:11

1.3k

Views

If $N = q^k n^2$ is an odd perfect number and $n < q^{k+1}$, does it follow that $k > 1$?

Published on 25 Mar 2026 - 12:50

score 293 · Answer 13 · 2014-04-25 15:46:37

293

Views

Can an odd perfect number be divisible by $5313$?

Published on 25 Apr 2014 - 15:46

score 438 · Answer 14 · 2014-05-06 20:26:05

438

Views

can't find the proof for the form of odd perfect numbers

Published on 06 May 2014 - 20:26

score 194 · Answer 15 · 2014-05-17 00:15:38

194

Views

A property for perfect numbers

Published on 17 May 2014 - 0:15

List Question

Are there (restricted) instances when the deficiency and sum-of-proper-divisors functions are multiplicative?

Does $2r - \sigma(r)$ divide $\sigma(r)$ if $r$ is deficient-perfect?

If $q^k n^2$ is an odd perfect number with special prime $q$, then does $(q+1)/2 \mid \sigma(n^2)$ hold?

Does $\gcd(r, \sigma(r)) = 2r - \sigma(r)$ always hold when $r$ is deficient-perfect?

What is wrong with my proof of there is no odd perfect number?

Question on Potential Relationship between Mertens Function and Perfect Number Counting Function

Conjecture That The Only Nearly Perfect Numbers Are The Powers Of 2

An interesting identity involving the abundancy index of divisors of odd perfect numbers

Are there any odd perfect numbers in base $g$, where $g \neq 10$?

Bounds for the abundancy index of divisors of odd perfect numbers in terms of the deficiency function

Perfect numbers and powers of two

If $N = q^k n^2$ is an odd perfect number and $n < q^{k+1}$, does it follow that $k > 1$?

Can an odd perfect number be divisible by $5313$?

can't find the proof for the form of odd perfect numbers

A property for perfect numbers

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