List questions from arithmetic-functions

Published on 31 Mar 2020 - 12:05

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Is there a number $\mathscr{D}_2 \neq \mathscr{D} = {{3003}^2}\cdot{22021}$ satisfying a certain condition?

Published on 04 Apr 2020 - 11:44

339

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Attempt to get a characterization of even perfect numbers from an equation involving the Dedekind psi function

Published on 14 Apr 2020 - 19:57

201

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Prove that for every $ϵ>0$ there exist infinitely many natural numbers $n$, such that $τ(n)\geq 2^{(1-ϵ)(\log(n)/\log(\log(n))}$.

Published on 15 Apr 2020 - 8:37

139

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On odd perfect numbers and a GCD - Part II

Published on 15 Apr 2020 - 10:22

134

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

Published on 16 Apr 2020 - 10:04

35

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Show this congruence holds

Published on 21 Apr 2020 - 2:19

304

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A question about Dirichlet series

Published on 25 Mar 2026 - 19:01

286

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Dirichlet Series in analytic number theory

Published on 25 Mar 2026 - 17:44

171

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Functions that link to divisor function

Published on 25 Mar 2026 - 14:19

267

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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

196

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

Published on 29 Apr 2020 - 6:10

90

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Showing that $\sum_{m=1}^{n}{\sigma(m)}=\sum_{k=1}^{n}{k\cdot \left\lfloor \frac n k\right\rfloor}$

Published on 03 May 2020 - 12:48

116

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Finding $f$ with Möbius inversion formula

Published on 25 Mar 2026 - 11:25

193

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Why is this arbitrary-looking identity of arithmetic functions "obvious"?

Published on 08 May 2020 - 20:02

List Question

Number of integers for which $\Omega=k$

Is there a number $\mathscr{D}_2 \neq \mathscr{D} = {{3003}^2}\cdot{22021}$ satisfying a certain condition?

Attempt to get a characterization of even perfect numbers from an equation involving the Dedekind psi function

Prove that for every $ϵ>0$ there exist infinitely many natural numbers $n$, such that $τ(n)\geq 2^{(1-ϵ)(\log(n)/\log(\log(n))}$.

On odd perfect numbers and a GCD - Part II

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

Show this congruence holds

A question about Dirichlet series

Dirichlet Series in analytic number theory

Functions that link to divisor function

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?

Showing that $\sum_{m=1}^{n}{\sigma(m)}=\sum_{k=1}^{n}{k\cdot \left\lfloor \frac n k\right\rfloor}$

Finding $f$ with Möbius inversion formula

Why is this arbitrary-looking identity of arithmetic functions "obvious"?

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