Question

Sum of positive divisors if and only if perfect square

score 2k · Answer 1 · 2017-10-30 22:21:25

2k

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Sum of positive divisors if and only if perfect square

Published on 30 Oct 2017 - 22:21

score 217 · Answer 2 · 2017-11-04 19:52:44

217

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Rigorous proof of $n\sum_{d\mid n}\frac{1}{d}=\sum_{d\mid n}d$ for $n\in\mathbb N$.

Published on 04 Nov 2017 - 19:52

score 110 · Answer 3 · 2017-11-12 00:35:47

110

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How factorize a lot of "little" numbers?

Published on 12 Nov 2017 - 0:35

score 3.6k · Answer 4 · 2017-11-16 15:31:17

3.6k

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find all positive integers n with $\sigma(n)=12$

Published on 16 Nov 2017 - 15:31

score 88 · Answer 5 · 2017-11-19 09:50:49

88

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A sum on co-prime positive integers with different parity

Published on 19 Nov 2017 - 9:50

score 1.1k · Answer 6 · 2026-03-26 09:46:55

1.1k

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Find all $n \in \mathbb N$ such that $\sigma(n) + \phi(n) = n\tau(n)$

Published on 26 Mar 2026 - 9:46

score 1k · Answer 7 · 2017-11-21 11:02:34

1k

Views

Show that every prime power if deficient.

Published on 21 Nov 2017 - 11:02

score 58 · Answer 8 · 2017-11-24 05:56:29

58

Views

Prove that if $\sigma_x(n) = \sigma_x(m)$ and $\sigma_{-x}(n) = \sigma_{-x}(m)$, then $n=m$.

Published on 24 Nov 2017 - 5:56

score 178 · Answer 9 · 2017-11-30 22:13:04

178

Views

On Rassias' conjecture and $\varphi(x)(1+\varphi(y))=\sigma(z)$, with $\varphi(n)$ the Euler's totient function and $\sigma(n)$ the sum of divisors

Published on 30 Nov 2017 - 22:13

score 123 · Answer 10 · 2026-03-26 09:42:35

123

Views

A different type of sum of divisors

Published on 26 Mar 2026 - 9:42

score 473 · Answer 11 · 2026-03-26 04:14:39

473

Views

How to do a sum of a function over all divisors of an integer with Maple?

Published on 26 Mar 2026 - 4:14

score 438 · Answer 12 · 2017-12-12 21:44:18

438

Views

On the equation $(\sigma(ab))^2=2a^2(\sigma(b))^2+2b^2(\sigma(a))^2$, for integers $1<a<b$

Published on 12 Dec 2017 - 21:44

score 131 · Answer 13 · 2017-12-17 20:15:23

131

Views

A proof of a statement deduced from Firoozbakht's conjecture and the definition of the sum of divisors function, and an optional question

Published on 17 Dec 2017 - 20:15

score 310 · Answer 14 · 2017-12-23 23:01:29

310

Views

How to show that $\sigma(n)=k$ has a finite # of solutions $k\in\mathbb{N}$?

Published on 23 Dec 2017 - 23:01

score 213 · Answer 15 · 2026-03-26 11:00:58

213

Views

Equivalent formula for the sum of first $n$ values of the number of divisors function

Published on 26 Mar 2026 - 11:00

List Question

Sum of positive divisors if and only if perfect square

Rigorous proof of $n\sum_{d\mid n}\frac{1}{d}=\sum_{d\mid n}d$ for $n\in\mathbb N$.

How factorize a lot of "little" numbers?

find all positive integers n with $\sigma(n)=12$

A sum on co-prime positive integers with different parity

Find all $n \in \mathbb N$ such that $\sigma(n) + \phi(n) = n\tau(n)$

Show that every prime power if deficient.

Prove that if $\sigma_x(n) = \sigma_x(m)$ and $\sigma_{-x}(n) = \sigma_{-x}(m)$, then $n=m$.

On Rassias' conjecture and $\varphi(x)(1+\varphi(y))=\sigma(z)$, with $\varphi(n)$ the Euler's totient function and $\sigma(n)$ the sum of divisors

A different type of sum of divisors

How to do a sum of a function over all divisors of an integer with Maple?

On the equation $(\sigma(ab))^2=2a^2(\sigma(b))^2+2b^2(\sigma(a))^2$, for integers $1<a<b$

A proof of a statement deduced from Firoozbakht's conjecture and the definition of the sum of divisors function, and an optional question

How to show that $\sigma(n)=k$ has a finite # of solutions $k\in\mathbb{N}$?

Equivalent formula for the sum of first $n$ values of the number of divisors function

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