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 58 · Answer 2 · 2026-03-19 21:45:02

58

Views

Characterize solutions of an equation involving the sum of divisors function and the Euler's totient function: Mersenne primes and Wagstaff primes

Published on 19 Mar 2026 - 21:45

score 201 · Answer 3 · 2026-03-24 03:32:28

201

Views

Heuristics on the asymptotic behaviour of the divisor funcion

Published on 24 Mar 2026 - 3:32

score 218 · Answer 4 · 2026-03-20 02:52:41

218

Views

What is the sum of reciprocal of product of $n$ primes?

Published on 20 Mar 2026 - 2:52

score 174 · Answer 5 · 2026-03-20 04:55:18

174

Views

A reference request about the closed-form of $\sum_{n=1}^\infty\frac{\sigma(n^2)}{n^6}$, where $\sigma(n)$ denotes the sum of divisors functions

Published on 20 Mar 2026 - 4:55

score 271 · Answer 6 · 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 331 · Answer 7 · 2026-03-22 05:37:01

331

Views

Sum of non-trivial divisors of number equals number itself

Published on 22 Mar 2026 - 5:37

score 662 · Answer 8 · 2026-03-22 05:46:26

662

Views

On the sum of divisors function.

Published on 22 Mar 2026 - 5:46

score 1k · Answer 9 · 2026-03-20 19:46:45

1k

Views

$\sigma(n) \equiv 1 \space \pmod{n}$ if and only if $n$ is prime

Published on 20 Mar 2026 - 19:46

score 56 · Answer 10 · 2026-03-22 06:06:47

56

Views

Show that for $n\gt 2$, $\frac{\sigma_1(n)}{n}\lt H_n$

Published on 22 Mar 2026 - 6:06

score 76 · Answer 11 · 2026-03-22 12:23:01

76

Views

Arithmetics: Number of divisors of an positive integer, their sum and product

Published on 22 Mar 2026 - 12:23

score 113 · Answer 12 · 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 183 · Answer 13 · 2026-03-16 23:45:42

183

Views

If $\frac{σ(x)}{x}=\frac{p+2}p$ where $p$ is an odd prime, does it follow that $x$ is an odd square?

Published on 16 Mar 2026 - 23:45

score 194 · Answer 14 · 2026-03-17 05:45:49

194

Views

Solutions of $\varphi\left(n^n\sigma(n)\right)=\varphi(n^{n+1})$, where $\sigma(n)$ is the sum of divisors and $\varphi(n)$ the Euler's totient

Published on 17 Mar 2026 - 5:45

score 69 · Answer 15 · 2026-03-17 05:16:32

69

Views

Divide $9536$ with a number in order to have an integer as result

Published on 17 Mar 2026 - 5:16

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

Characterize solutions of an equation involving the sum of divisors function and the Euler's totient function: Mersenne primes and Wagstaff primes

Heuristics on the asymptotic behaviour of the divisor funcion

What is the sum of reciprocal of product of $n$ primes?

A reference request about the closed-form of $\sum_{n=1}^\infty\frac{\sigma(n^2)}{n^6}$, where $\sigma(n)$ denotes the sum of divisors functions

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

Sum of non-trivial divisors of number equals number itself

On the sum of divisors function.

$\sigma(n) \equiv 1 \space \pmod{n}$ if and only if $n$ is prime

Show that for $n\gt 2$, $\frac{\sigma_1(n)}{n}\lt H_n$

Arithmetics: Number of divisors of an positive integer, their sum and product

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

If $\frac{σ(x)}{x}=\frac{p+2}p$ where $p$ is an odd prime, does it follow that $x$ is an odd square?

Solutions of $\varphi\left(n^n\sigma(n)\right)=\varphi(n^{n+1})$, where $\sigma(n)$ is the sum of divisors and $\varphi(n)$ the Euler's totient

Divide $9536$ with a number in order to have an integer as result

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