Question

Question about $\varphi(n)+n\mid \sigma(n)$

score 49 · Answer 1 · 2026-03-27 18:35:48

49

Views

Question about $\varphi(n)+n\mid \sigma(n)$

Published on 27 Mar 2026 - 18:35

score 135 · Answer 2 · 2026-03-26 02:45:40

135

Views

When does $\gcd(m,\sigma(m^2))$ equal $\gcd(m^2,\sigma(m^2))$? What are the exceptions?

Published on 26 Mar 2026 - 2:45

score 227 · Answer 3 · 2020-04-17 11:25:54

227

Views

What is the asymptotic density of positive integers $n$ satisfying $\gcd(n,\sigma(n^2))=\gcd(n^2,\sigma(n^2))$?

Published on 17 Apr 2020 - 11:25

score 76 · Answer 4 · 2026-02-23 02:57:41

76

Views

Odd perfect numbers having as prime factors exclusively Mersenne primes and Fermat primes: reference request or proposal as an exercise

Published on 23 Feb 2026 - 2:57

score 53 · Answer 5 · 2026-03-26 05:54:36

53

Views

Question about a result on odd perfect numbers - Part II

Published on 26 Mar 2026 - 5:54

score 267 · Answer 6 · 2026-03-25 10:59:03

267

Views

If an arithmetic function $f$ satisfies $f(mn) \leq f(m)f(n)$ (whenever $\gcd(m,n)=1$), is $f$ weakly multiplicative or submultiplicative?

Published on 25 Mar 2026 - 10:59

score 197 · Answer 7 · 2026-03-26 02:48:57

197

Views

Can this inequality involving the deficiency and sum of aliquot divisors be improved?

Published on 26 Mar 2026 - 2:48

score 105 · Answer 8 · 2026-03-25 14:21:07

105

Views

Stuck with number theory identity about the divisor function

Published on 25 Mar 2026 - 14:21

score 213 · Answer 9 · 2026-03-27 23:35:30

213

Views

On variations of a claim due to Kaneko in terms of Lehmer means

Published on 27 Mar 2026 - 23:35

score 75 · Answer 10 · 2026-03-25 17:40:14

75

Views

What is meant by $\sum_{d \le x}f(d)$ in this equation?

Published on 25 Mar 2026 - 17:40

score 92 · Answer 11 · 2020-05-23 20:43:10

92

Views

Simplify $\sum_{k = 1}^{\left\lfloor{N/2}\right\rfloor} \sum_{i = 1}^{k} \sum_{d_1, d_2 = 1}^{N} \left[{{d}_{1}\, {d}_{2} = i (2\, k - i)}\right]$

Published on 23 May 2020 - 20:43

score 288 · Answer 12 · 2026-03-26 05:54:36

288

Views

On odd perfect numbers and a GCD - Part III

Published on 26 Mar 2026 - 5:54

score 150 · Answer 13 · 2020-06-03 11:36:14

150

Views

prove that $ \frac{\sigma(1)}{1}+\frac{\sigma(2)}{2}+\dots+\frac{\sigma(n)}{n} \leq 2 n $

Published on 03 Jun 2020 - 11:36

score 100 · Answer 14 · 2020-06-11 05:05:29

100

Views

The summation $\sum_{n\geqslant1} \frac1n\sum_{d\mid n}\frac{d}{n^2+d}.$

Published on 11 Jun 2020 - 5:05

score 114 · Answer 15 · 2026-03-27 12:16:55

114

Views

Conjecture on the sum of prime factors

Published on 27 Mar 2026 - 12:16

List Question

Question about $\varphi(n)+n\mid \sigma(n)$

When does $\gcd(m,\sigma(m^2))$ equal $\gcd(m^2,\sigma(m^2))$? What are the exceptions?

What is the asymptotic density of positive integers $n$ satisfying $\gcd(n,\sigma(n^2))=\gcd(n^2,\sigma(n^2))$?

Odd perfect numbers having as prime factors exclusively Mersenne primes and Fermat primes: reference request or proposal as an exercise

Question about a result on odd perfect numbers - Part II

If an arithmetic function $f$ satisfies $f(mn) \leq f(m)f(n)$ (whenever $\gcd(m,n)=1$), is $f$ weakly multiplicative or submultiplicative?

Can this inequality involving the deficiency and sum of aliquot divisors be improved?

Stuck with number theory identity about the divisor function

On variations of a claim due to Kaneko in terms of Lehmer means

What is meant by $\sum_{d \le x}f(d)$ in this equation?

Simplify $\sum_{k = 1}^{\left\lfloor{N/2}\right\rfloor} \sum_{i = 1}^{k} \sum_{d_1, d_2 = 1}^{N} \left[{{d}_{1}\, {d}_{2} = i (2\, k - i)}\right]$

On odd perfect numbers and a GCD - Part III

prove that $ \frac{\sigma(1)}{1}+\frac{\sigma(2)}{2}+\dots+\frac{\sigma(n)}{n} \leq 2 n $

The summation $\sum_{n\geqslant1} \frac1n\sum_{d\mid n}\frac{d}{n^2+d}.$

Conjecture on the sum of prime factors

Trending Questions

Popular # Hahtags

Popular Questions