Question

If $N = {q^k}{n^2}$ is an odd perfect number given in Eulerian form, does $\sigma(n^2)/q$ divide $2n^2 - \sigma(n^2)$?

score 45 · Answer 1 · 2026-03-26 22:16:14

45

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If $N = {q^k}{n^2}$ is an odd perfect number given in Eulerian form, does $\sigma(n^2)/q$ divide $2n^2 - \sigma(n^2)$?

Published on 26 Mar 2026 - 22:16

score 187 · Answer 2 · 2026-03-27 17:06:31

187

Views

Can you prove this identity involving the divisor sum function?

Published on 27 Mar 2026 - 17:06

score 74 · Answer 3 · 2016-02-13 15:13:50

74

Views

Is $\sigma(2^r)$ a palindrome (in base $10$) for some $r > 2$, where $\sigma$ is the sum-of-divisors function?

Published on 13 Feb 2016 - 15:13

score 56 · Answer 4 · 2016-02-15 11:24:41

56

Views

Closed form for $f(n)=\sum_{d\mid n}(-1)^{d}.d$?

Published on 15 Feb 2016 - 11:24

score 383 · Answer 5 · 2026-03-29 14:17:15

383

Views

Writing partition function with divisor function

Published on 29 Mar 2026 - 14:17

score 378 · Answer 6 · 2026-03-26 12:07:05

378

Views

Exploring the Dirichlet series of the sum of remainder function

Published on 26 Mar 2026 - 12:07

score 47 · Answer 7 · 2016-02-20 21:53:39

47

Views

If $\sigma _{1}(n)\mid \sigma _{2}(n)$, does $n$ has to be a perfect square?

Published on 20 Feb 2016 - 21:53

score 114 · Answer 8 · 2026-03-27 00:06:37

114

Views

Does the Descartes number $D = 198585576189$ have a friend?

Published on 27 Mar 2026 - 0:06

score 64 · Answer 9 · 2026-03-25 12:26:05

64

Views

A computational experiment about identities involving the sum of remainders function

Published on 25 Mar 2026 - 12:26

score 62 · Answer 10 · 2016-03-08 03:04:26

62

Views

What is wrong with this proof that $p_1 > \omega(x)$, where $p_1$ is the least prime dividing $x$?

Published on 08 Mar 2016 - 3:04

score 111 · Answer 11 · 2016-03-16 11:22:05

111

Views

Equation involving 'sigma of integer' function

Published on 16 Mar 2016 - 11:22

score 129 · Answer 12 · 2026-03-26 04:36:32

129

Views

Has limit $\frac{\sigma_0(n)\sigma_2(n)}{(\sigma(n))^2H_n},$ where $H_n$ is the nth harmonic number?

Published on 26 Mar 2026 - 4:36

score 257 · Answer 13 · 2026-03-27 17:06:11

257

Views

Is the following inequality involving the sum-of-divisors and Euler totient functions true?

Published on 27 Mar 2026 - 17:06

score 139 · Answer 14 · 2026-03-26 22:19:35

139

Views

Has it been proved that odd perfect numbers cannot be triangular?

Published on 26 Mar 2026 - 22:19

score 114 · Answer 15 · 2026-03-26 22:13:14

114

Views

Even perfect numbers and a relationship with polygonal numbers

Published on 26 Mar 2026 - 22:13

List Question

If $N = {q^k}{n^2}$ is an odd perfect number given in Eulerian form, does $\sigma(n^2)/q$ divide $2n^2 - \sigma(n^2)$?

Can you prove this identity involving the divisor sum function?

Is $\sigma(2^r)$ a palindrome (in base $10$) for some $r > 2$, where $\sigma$ is the sum-of-divisors function?

Closed form for $f(n)=\sum_{d\mid n}(-1)^{d}.d$?

Writing partition function with divisor function

Exploring the Dirichlet series of the sum of remainder function

If $\sigma _{1}(n)\mid \sigma _{2}(n)$, does $n$ has to be a perfect square?

Does the Descartes number $D = 198585576189$ have a friend?

A computational experiment about identities involving the sum of remainders function

What is wrong with this proof that $p_1 > \omega(x)$, where $p_1$ is the least prime dividing $x$?

Equation involving 'sigma of integer' function

Has limit $\frac{\sigma_0(n)\sigma_2(n)}{(\sigma(n))^2H_n},$ where $H_n$ is the nth harmonic number?

Is the following inequality involving the sum-of-divisors and Euler totient functions true?

Has it been proved that odd perfect numbers cannot be triangular?

Even perfect numbers and a relationship with polygonal numbers

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