List questions from arithmetic-functions

Published on 25 Mar 2026 - 2:57

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Is it possible to simplify this expression even further?

Published on 25 Mar 2026 - 4:38

54

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Help proving an equality about arithmetic functions

Published on 21 Jun 2018 - 16:25

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If an arithmetic function $f$ is such that $\sum\limits_{n=1}^Nf(n)=\Theta(N)$ then $f(n)=o(n^\epsilon)$

Published on 25 Jun 2018 - 16:46

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Number of pairs $(a,b)$ such that $a+b<n$ and such that $\gcd(a,b,n)=1$

Published on 17 Jul 2018 - 17:07

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Are there any other squares $n^2$ for which $\gcd(n^2, \sigma(n^2)) = 2n^2 - \sigma(n^2)$?

Published on 04 Sep 2018 - 8:28

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Can you explain the following property for arithmetic functions.

Published on 04 Sep 2018 - 16:42

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Is $(q^k n^2 \text{ is perfect }) \iff (D(q^k)D(n^2) = 2s(q^k)s(n^2))$ only true for odd perfect numbers $q^k n^2$?

Published on 02 Oct 2018 - 7:44

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What is the common (and simplified) value for $D(q^k)D(n^2) = 2s(q^k)s(n^2)$ when $q^k n^2$ is an odd perfect number?

Published on 02 Oct 2018 - 11:26

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Von Mangoldt function with PARI GP

Published on 25 Mar 2026 - 2:57

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Does mathlove's answer imply that $D(n^2) \mid n^2$?

Published on 18 Oct 2018 - 11:53

162

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Could a Fermat prime divide an odd perfect number?

Published on 18 Oct 2018 - 15:09

173

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If $x$ and $y$ are solitary numbers satisfying $\gcd(x,y)=1$, under what conditions does it follow that $xy$ is also solitary?

Published on 30 Oct 2018 - 4:22

55

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Möbius inversion across all natural numbers (no divisors)

Published on 23 Mar 2026 - 3:00

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How to prove $\sum_{d\mid q}\frac{\mu(d)\log d}{d}=-\frac{\phi(q)}{q}\sum_{p\mid q}\frac{\log p}{p-1}$?

Published on 12 Nov 2018 - 5:23

List Question

A conjecture regarding odd perfect numbers

Is it possible to simplify this expression even further?

Help proving an equality about arithmetic functions

If an arithmetic function $f$ is such that $\sum\limits_{n=1}^Nf(n)=\Theta(N)$ then $f(n)=o(n^\epsilon)$

Number of pairs $(a,b)$ such that $a+b<n$ and such that $\gcd(a,b,n)=1$

Are there any other squares $n^2$ for which $\gcd(n^2, \sigma(n^2)) = 2n^2 - \sigma(n^2)$?

Can you explain the following property for arithmetic functions.

Is $(q^k n^2 \text{ is perfect }) \iff (D(q^k)D(n^2) = 2s(q^k)s(n^2))$ only true for odd perfect numbers $q^k n^2$?

What is the common (and simplified) value for $D(q^k)D(n^2) = 2s(q^k)s(n^2)$ when $q^k n^2$ is an odd perfect number?

Von Mangoldt function with PARI GP

Does mathlove's answer imply that $D(n^2) \mid n^2$?

Could a Fermat prime divide an odd perfect number?

If $x$ and $y$ are solitary numbers satisfying $\gcd(x,y)=1$, under what conditions does it follow that $xy$ is also solitary?

Möbius inversion across all natural numbers (no divisors)

How to prove $\sum_{d\mid q}\frac{\mu(d)\log d}{d}=-\frac{\phi(q)}{q}\sum_{p\mid q}\frac{\log p}{p-1}$?

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