List questions from arithmetic-functions

Published on 26 Nov 2018 - 15:02

376

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A proof of $\sum\limits_{d|n} \sigma(d) = n \sum\limits_{d|n} {\tau(d) \over d}$

Published on 27 Nov 2018 - 14:46

76

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What proportion of the positive integers satisfies $\gcd(n^2,\sigma(n^2))>\sigma(n)$, where $\sigma$ is the sum-of-divisors function?

Published on 28 Nov 2018 - 14:47

793

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About The Sum of Positive Divisors of $n$

Published on 22 Mar 2026 - 10:42

202

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On Yanqi Xu's 2016 joint undergraduate math research project with Dr. Judy Holdener at Kenyon College

Published on 03 Jan 2019 - 10:36

148

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On $\sup|\varphi^{-1}(n)|=+\infty$

Published on 25 Mar 2026 - 5:59

67

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If $q \equiv k \equiv 1 \pmod 4$, is it necessarily true that $\gcd\bigg(\sigma(q^k),\sigma(q^{(k-1)/2})\bigg)=1$?

Published on 06 Jan 2019 - 1:59

336

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On Basak's "Bounds On Factors Of Odd Perfect Numbers"

Published on 08 Jan 2019 - 8:03

50

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How to simplify $2 q^{\frac{k-1}{2}} n^2 - \sigma(q^{\frac{k-1}{2}})\sigma(n^2)$

Published on 14 Jan 2019 - 7:04

45

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If $\sigma(n) = 2n - d$ and $d \mid n$, is it true that $d = \gcd(n,\sigma(n))$?

Published on 14 Jan 2019 - 10:06

63

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Probability of $f(n) - \varphi(n)$ to be an even number.

Published on 20 Jan 2019 - 5:04

158

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If $\sigma(n)/n = 5/3$, then $5 \nmid n$. Does it also follow that $3 \nmid \sigma(n)$?

Published on 08 Feb 2019 - 6:15

73

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Estimating of Big Omega function

Published on 19 Feb 2019 - 18:04

71

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Let a be an multiplicative arithmetic function. Show: either $a(1) = 1$ or $a(1) = 0$. Show that if $a(1) = 0$ then $a(n) = 0$ for all $n$

Published on 02 Mar 2019 - 17:02

123

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Breaking the barriers at $q=5$ and $q=13$ for $q^k n^2$ an odd perfect number with special prime $q$

Published on 10 Mar 2019 - 10:59

List Question

A question regarding a paper of Ochem and Rao about the radical of an odd perfect number

A proof of $\sum\limits_{d|n} \sigma(d) = n \sum\limits_{d|n} {\tau(d) \over d}$

What proportion of the positive integers satisfies $\gcd(n^2,\sigma(n^2))>\sigma(n)$, where $\sigma$ is the sum-of-divisors function?

About The Sum of Positive Divisors of $n$

On Yanqi Xu's 2016 joint undergraduate math research project with Dr. Judy Holdener at Kenyon College

On $\sup|\varphi^{-1}(n)|=+\infty$

If $q \equiv k \equiv 1 \pmod 4$, is it necessarily true that $\gcd\bigg(\sigma(q^k),\sigma(q^{(k-1)/2})\bigg)=1$?

On Basak's "Bounds On Factors Of Odd Perfect Numbers"

How to simplify $2 q^{\frac{k-1}{2}} n^2 - \sigma(q^{\frac{k-1}{2}})\sigma(n^2)$

If $\sigma(n) = 2n - d$ and $d \mid n$, is it true that $d = \gcd(n,\sigma(n))$?

Probability of $f(n) - \varphi(n)$ to be an even number.

If $\sigma(n)/n = 5/3$, then $5 \nmid n$. Does it also follow that $3 \nmid \sigma(n)$?

Estimating of Big Omega function

Let a be an multiplicative arithmetic function. Show: either $a(1) = 1$ or $a(1) = 0$. Show that if $a(1) = 0$ then $a(n) = 0$ for all $n$

Breaking the barriers at $q=5$ and $q=13$ for $q^k n^2$ an odd perfect number with special prime $q$

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