List questions from arithmetic-functions

Published on 02 Dec 2016 - 18:33

73

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Represent large integers with exponents.

Published on 08 Dec 2016 - 22:46

96

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On $\lambda(n)$.

Published on 14 Dec 2016 - 3:13

143

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Closed form for $\sum\limits_{d|n}\sigma(d)$?

Published on 25 Mar 2026 - 15:58

242

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Identity function that returns $1$ for the input $0$.

Published on 17 Dec 2016 - 23:45

681

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A GCD summation $\sum_{\gcd(i,n)=1} \gcd(i-1,n)$

Published on 01 Jan 2017 - 20:52

223

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Hints to deduce convergence of an infinite product to $e^{-x^2}$ on $(0,1)$, and for a numeric series involving number-theoretic functions

Published on 06 Jan 2017 - 0:00

121

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Perfect square is congruent to $n$ modulo $2^{12}$

Published on 08 Jan 2017 - 2:46

525

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Given that you only have multiplication and addition, how can you divide two numbers?

Published on 09 Jan 2017 - 16:03

83

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Does there exist an integer $m$ which is not in the image of $D(n)=2n - \sigma(n)$?

Published on 26 Mar 2026 - 9:17

200

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If $a$ is the arithmetic function with $\sum_{d\mid n}a(d)=2^n$, then $n\mid a(n)$

Published on 25 Mar 2026 - 13:05

64

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Is there a function $s(n)$ which tells the amount of factors any $n$ has?

Published on 25 Mar 2026 - 19:04

224

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How to integrate arithmetic functions?

Published on 25 Jan 2017 - 23:43

72

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A few questions about (partial) arithmetic derivative

Published on 16 Feb 2017 - 7:30

332

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Dirichlet product of arithmetic functions $\tau$ and $\sigma$

Published on 25 Mar 2026 - 19:03

List Question

Proving that a function is multiplicative.

Represent large integers with exponents.

On $\lambda(n)$.

Closed form for $\sum\limits_{d|n}\sigma(d)$?

Identity function that returns $1$ for the input $0$.

A GCD summation $\sum_{\gcd(i,n)=1} \gcd(i-1,n)$

Hints to deduce convergence of an infinite product to $e^{-x^2}$ on $(0,1)$, and for a numeric series involving number-theoretic functions

Perfect square is congruent to $n$ modulo $2^{12}$

Given that you only have multiplication and addition, how can you divide two numbers?

Does there exist an integer $m$ which is not in the image of $D(n)=2n - \sigma(n)$?

If $a$ is the arithmetic function with $\sum_{d\mid n}a(d)=2^n$, then $n\mid a(n)$

Is there a function $s(n)$ which tells the amount of factors any $n$ has?

How to integrate arithmetic functions?

A few questions about (partial) arithmetic derivative

Dirichlet product of arithmetic functions $\tau$ and $\sigma$

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