List questions from arithmetic-functions

Published on 20 Mar 2019 - 10:51

764

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$\sum_{d|n, d>0} (\sigma(d)/d)\mu(n/d))=1/n$

Published on 25 Mar 2019 - 18:22

154

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On the proof that $\phi(n)/n$ has a limit law

Published on 03 Apr 2019 - 5:10

226

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Determine a property of $S_b(n)$, which is the sum of the digits of $n$ when $n$ is expressed in base $b$

Published on 08 Apr 2019 - 7:05

84

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Simplifying expression Mobius Function

Published on 25 Mar 2026 - 8:03

230

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Which root lattices have a theta series with this property?

Published on 25 Mar 2026 - 3:01

146

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Does this conjecture imply the prime number theorem?

Published on 26 Apr 2019 - 16:24

165

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How many numbers with no common divisor are there?

Published on 26 May 2019 - 12:12

67

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Probability that two integers have the very same amount of prime factors

Published on 30 May 2019 - 21:21

92

Views

Can any Power function (whose base is not zero) , e.g. $2^{n}$, be defined arithmetically (i.e. using addition and multiplication only)?

Published on 25 Mar 2026 - 7:40

188

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Quadratic Gauss Sum with Jacobi Symbol of even nonsquare free Modulus

Published on 25 Mar 2026 - 8:11

100

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prove the formula where $n=\prod_{i=1}^k p_{i}^{\alpha_i}$

Published on 17 Jun 2019 - 12:34

37

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Closed-form for $F(n) = \sum_{d|n} \omega_x(d) $

Published on 25 Mar 2026 - 9:26

80

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How often is $N/(2N-\sigma(N))$ a palindrome (in base-$10$) if $N$ is deficient-perfect?

Published on 25 Mar 2026 - 6:06

81

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Are there (restricted) instances when the deficiency and sum-of-proper-divisors functions are multiplicative?

Published on 24 Mar 2026 - 3:03

List Question

Another sum involving totient function or gcd

$\sum_{d|n, d>0} (\sigma(d)/d)\mu(n/d))=1/n$

On the proof that $\phi(n)/n$ has a limit law

Determine a property of $S_b(n)$, which is the sum of the digits of $n$ when $n$ is expressed in base $b$

Simplifying expression Mobius Function

Which root lattices have a theta series with this property?

Does this conjecture imply the prime number theorem?

How many numbers with no common divisor are there?

Probability that two integers have the very same amount of prime factors

Can any Power function (whose base is not zero) , e.g. $2^{n}$, be defined arithmetically (i.e. using addition and multiplication only)?

Quadratic Gauss Sum with Jacobi Symbol of even nonsquare free Modulus

prove the formula where $n=\prod_{i=1}^k p_{i}^{\alpha_i}$

Closed-form for $F(n) = \sum_{d|n} \omega_x(d) $

How often is $N/(2N-\sigma(N))$ a palindrome (in base-$10$) if $N$ is deficient-perfect?

Are there (restricted) instances when the deficiency and sum-of-proper-divisors functions are multiplicative?

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