Question

On the representation $\Gamma(z)=\sum_{n=2}^\infty \int_0^\infty a(n)e^{-e^{nx}}e^{nzx}dx$, for arithmetic functions $a(n)$ and $\Re z>0$

score 204 · Answer 1 · 2026-03-26 13:01:00

204

Views

On the representation $\Gamma(z)=\sum_{n=2}^\infty \int_0^\infty a(n)e^{-e^{nx}}e^{nzx}dx$, for arithmetic functions $a(n)$ and $\Re z>0$

Published on 26 Mar 2026 - 13:01

score 793 · Answer 2 · 2017-02-23 02:09:04

793

Views

Find all positive integers $n$ such that $\phi(\phi(n))=3$.

Published on 23 Feb 2017 - 2:09

score 19 · Answer 3 · 2017-02-26 05:57:37

19

Views

Are arithmetic operations independent of dimension?

Published on 26 Feb 2017 - 5:57

score 167 · Answer 4 · 2017-03-05 04:40:21

167

Views

Identity related to the totient function:$\sum\limits_{k=1}^n\phi(k)\left\lfloor \frac{n}{k}\right\rfloor = \frac{n(n+1)}{2}$

Published on 05 Mar 2017 - 4:40

score 73 · Answer 5 · 2017-03-05 18:36:32

73

Views

Analysis of the ratio $D(n)/n$ (Reference request)

Published on 05 Mar 2017 - 18:36

score 105 · Answer 6 · 2017-03-08 21:23:44

105

Views

About the number of solutions of $\varphi(n)=m$

Published on 08 Mar 2017 - 21:23

score 58 · Answer 7 · 2017-03-22 12:28:27

58

Views

Why extra conditions to prove that $g(x) = \Sigma f(mx)$ and $f(x) = \Sigma \mu(n)g(nx)$ are equivalent

Published on 22 Mar 2017 - 12:28

score 3.7k · Answer 8 · 2017-03-23 01:32:19

3.7k

Views

Show that if $n$ is a positive integer with $r$ distinct odd prime factors, then $2^r \mid \varphi(n)$

Published on 23 Mar 2017 - 1:32

score 2.4k · Answer 9 · 2026-03-25 15:57:19

2.4k

Views

Dirichlet Convolution of the Mobius Function with Itself

Published on 25 Mar 2026 - 15:57

score 509 · Answer 10 · 2026-03-25 16:45:42

509

Views

Showing a nonzero multiplicative arithmetic function satisfies $f(1) = 1$

Published on 25 Mar 2026 - 16:45

score 636 · Answer 11 · 2017-03-27 00:09:52

636

Views

showing a function is multiplicative and not completely multiplicative

Published on 27 Mar 2017 - 0:09

score 183 · Answer 12 · 2017-04-03 01:00:59

183

Views

Solve $p(n)^2=\sigma(n)+423$ for $1<n<2012$

Published on 03 Apr 2017 - 1:00

score 48 · Answer 13 · 2026-03-25 16:45:42

48

Views

Solve de equation: σ(∅(n))=2^n

Published on 25 Mar 2026 - 16:45

score 73 · Answer 14 · 2017-04-07 07:10:29

73

Views

The excess of an integer $n$

Published on 07 Apr 2017 - 7:10

score 316 · Answer 15 · 2017-04-08 14:24:55

316

Views

Prove that the set of complex arithmetic functions is a domain

Published on 08 Apr 2017 - 14:24

List Question

On the representation $\Gamma(z)=\sum_{n=2}^\infty \int_0^\infty a(n)e^{-e^{nx}}e^{nzx}dx$, for arithmetic functions $a(n)$ and $\Re z>0$

Find all positive integers $n$ such that $\phi(\phi(n))=3$.

Are arithmetic operations independent of dimension?

Identity related to the totient function:$\sum\limits_{k=1}^n\phi(k)\left\lfloor \frac{n}{k}\right\rfloor = \frac{n(n+1)}{2}$

Analysis of the ratio $D(n)/n$ (Reference request)

About the number of solutions of $\varphi(n)=m$

Why extra conditions to prove that $g(x) = \Sigma f(mx)$ and $f(x) = \Sigma \mu(n)g(nx)$ are equivalent

Show that if $n$ is a positive integer with $r$ distinct odd prime factors, then $2^r \mid \varphi(n)$

Dirichlet Convolution of the Mobius Function with Itself

Showing a nonzero multiplicative arithmetic function satisfies $f(1) = 1$

showing a function is multiplicative and not completely multiplicative

Solve $p(n)^2=\sigma(n)+423$ for $1<n<2012$

Solve de equation: σ(∅(n))=2^n

The excess of an integer $n$

Prove that the set of complex arithmetic functions is a domain

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