Question

Could we predict the exact value of $\sum_{n\geq 0}\dfrac{1}{\sigma(n!)}$ while it is convergent?

score 37 · Answer 1 · 2019-07-25 07:36:34

37

Views

Could we predict the exact value of $\sum_{n\geq 0}\dfrac{1}{\sigma(n!)}$ while it is convergent?

Published on 25 Jul 2019 - 7:36

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 158 · Answer 3 · 2019-08-03 13:34:47

158

Views

For the divisor function is $d(n^2)$ related to $d(n)$ knowing also n?

Published on 03 Aug 2019 - 13:34

score 45 · Answer 4 · 2019-08-03 14:00:05

45

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 03 Aug 2019 - 14:00

score 27 · Answer 5 · 2019-08-11 11:34:35

27

Views

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

Published on 11 Aug 2019 - 11:34

score 52 · Answer 6 · 2019-08-13 13:38:13

52

Views

Possible Upper Bound of Sum of Divisors

Published on 13 Aug 2019 - 13:38

score 216 · Answer 7 · 2019-08-28 21:26:33

216

Views

Question about Certain Upper Bounds of the Sum of Divisors Function

Published on 28 Aug 2019 - 21:26

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 65 · Answer 9 · 2019-09-15 15:40:38

65

Views

Partial Divisor Summatory Function Calculation

Published on 15 Sep 2019 - 15:40

score 465 · Answer 10 · 2019-09-15 20:08:49

465

Views

On the sum of sum of divisors $\sum_{a=1}^{N} D \left({\left\lfloor{\frac{N}{a}}\right\rfloor}\right)$.

Published on 15 Sep 2019 - 20:08

score 142 · Answer 11 · 2019-09-21 08:34:41

142

Views

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

Published on 21 Sep 2019 - 8:34

score 84 · Answer 12 · 2026-03-25 07:42:09

84

Views

Alternate method to derive the following equation

Published on 25 Mar 2026 - 7:42

score 84 · Answer 13 · 2026-03-25 11:14:57

84

Views

How to prove that $\sigma_{k+1}(n) = \sum\limits_{d|n}d^k \cdot\phi(d)\cdot\sigma_{k}(\frac{n}{d})$

Published on 25 Mar 2026 - 11:14

score 509 · Answer 14 · 2014-03-27 08:56:43

509

Views

Explanation for a theorem pertaining on Dirichlet character sums

Published on 27 Mar 2014 - 8:56

score 1.1k · Answer 15 · 2014-04-08 18:08:18

1.1k

Views

How can I prove that $\frac{\sigma(n)}{n} = \sum_{(d|n)} \frac{1}{d}$ for every $n \in \mathbb{Z^{+}}$?

Published on 08 Apr 2014 - 18:08

List Question

Could we predict the exact value of $\sum_{n\geq 0}\dfrac{1}{\sigma(n!)}$ while it is convergent?

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

For the divisor function is $d(n^2)$ related to $d(n)$ knowing also n?

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?

Possible Upper Bound of Sum of Divisors

Question about Certain Upper Bounds of the Sum of Divisors Function

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

Partial Divisor Summatory Function Calculation

On the sum of sum of divisors $\sum_{a=1}^{N} D \left({\left\lfloor{\frac{N}{a}}\right\rfloor}\right)$.

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

Alternate method to derive the following equation

How to prove that $\sigma_{k+1}(n) = \sum\limits_{d|n}d^k \cdot\phi(d)\cdot\sigma_{k}(\frac{n}{d})$

Explanation for a theorem pertaining on Dirichlet character sums

How can I prove that $\frac{\sigma(n)}{n} = \sum_{(d|n)} \frac{1}{d}$ for every $n \in \mathbb{Z^{+}}$?

Trending Questions

Popular # Hahtags

Popular Questions