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 80 · Answer 1 · 2026-05-05 11:55:20

80

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 05 May 2026 - 11:55

score 67 · Answer 2 · 2026-05-07 11:33:09

67

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 07 May 2026 - 11:33

score 208 · Answer 3 · 2026-05-07 13:31:33

208

Views

Heuristics on the asymptotic behaviour of the divisor funcion

Published on 07 May 2026 - 13:31

score 230 · Answer 4 · 2026-05-07 19:12:44

230

Views

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

Published on 07 May 2026 - 19:12

score 187 · Answer 5 · 2026-04-29 12:34:36

187

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 29 Apr 2026 - 12:34

score 280 · Answer 6 · 2026-05-07 07:35:38

280

Views

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

Published on 07 May 2026 - 7:35

score 342 · Answer 7 · 2026-05-07 10:10:06

342

Views

Sum of non-trivial divisors of number equals number itself

Published on 07 May 2026 - 10:10

score 673 · Answer 8 · 2026-05-10 12:25:50

673

Views

On the sum of divisors function.

Published on 10 May 2026 - 12:25

score 1k · Answer 9 · 2026-04-29 12:24:22

1k

Views

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

Published on 29 Apr 2026 - 12:24

score 64 · Answer 10 · 2026-04-29 12:16:22

64

Views

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

Published on 29 Apr 2026 - 12:16

score 86 · Answer 11 · 2026-05-10 09:56:07

86

Views

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

Published on 10 May 2026 - 9:56

score 125 · Answer 12 · 2026-05-07 12:42:02

125

Views

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

Published on 07 May 2026 - 12:42

score 190 · Answer 13 · 2026-05-10 12:55:17

190

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 10 May 2026 - 12:55

score 206 · Answer 14 · 2026-05-10 12:55:14

206

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 10 May 2026 - 12:55

score 79 · Answer 15 · 2026-05-10 12:53:41

79

Views

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

Published on 10 May 2026 - 12:53

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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