Question

Looking an asymptotic for $\sum_{k\leq x}\Lambda(k)e^k$, where $\Lambda (n)$ is the von Mangoldt function

score 301 · Answer 1 · 2026-02-24 00:46:46

301

Views

Looking an asymptotic for $\sum_{k\leq x}\Lambda(k)e^k$, where $\Lambda (n)$ is the von Mangoldt function

Published on 24 Feb 2026 - 0:46

score 774 · Answer 2 · 2026-02-24 00:48:11

774

Views

LCM of binomial coefficients and related functions

Published on 24 Feb 2026 - 0:48

score 283 · Answer 3 · 2026-03-25 21:22:06

283

Views

Number of zeros of a polynomial modulo n is a multiplicative function

Published on 25 Mar 2026 - 21:22

score 121 · Answer 4 · 2015-10-06 18:51:50

121

Views

On Abel summation $\sum_{e<n\leq x}\left(\mu(n)\cdot\int_2^n\frac{ds}{\log s}\right)$, where $\mu(n)$ is the Möbius function

Published on 06 Oct 2015 - 18:51

score 660 · Answer 5 · 2015-10-16 20:52:45

660

Views

Arithmetic Derivative

Published on 16 Oct 2015 - 20:52

score 592 · Answer 6 · 2026-03-08 08:50:57

592

Views

Formula with $\sigma(n)$ and $\phi(n)$ is not an integer if $n$ is not square-free

Published on 08 Mar 2026 - 8:50

score 160 · Answer 7 · 2015-10-27 14:36:07

160

Views

The sum $\sum_{n\leq x}\sum_{\substack{1\leq k\leq n \\ gdc(k,n)=1}}\cos^2\pi \frac{k}{n}$ diverges as $x$, when $x$ tends to infitity

Published on 27 Oct 2015 - 14:36

score 56 · Answer 8 · 2015-11-02 07:01:22

56

Views

On $\sigma(n)<n+\frac{n}{2}\log\frac{n+1}{n-1}+\frac{n}{4} \left(\sum_{\substack{d|n,1<d<n}}\log\frac{(n+d)(n+1)}{(n-d)(n-1)}\right)$

Published on 02 Nov 2015 - 7:01

score 47 · Answer 9 · 2015-11-10 07:54:02

47

Views

Numbers $n$ whose prime factors are $2$ and $5$ if and only if $\sum_{k=1}^{rad(n)}\mu(k)k=0$?

Published on 10 Nov 2015 - 7:54

score 228 · Answer 10 · 2015-11-12 03:37:46

Show that if $n$ is even then $\sum_{d|n}\mu(d)\phi(d)=0$ using only Dirichlet Convolution propertys (without multiplicative function concepts)

score 150 · Answer 11 · 2026-03-07 10:56:46

150

Views

Infinite sum of a function $g(n)=\sum_{d|n \; d\ne n}g(d)$

Published on 07 Mar 2026 - 10:56

score 320 · Answer 12 · 2026-03-26 21:12:01

320

Views

Using Dirichlet convolution where f = μ ∗ μ (Mobius) to find f(24)?

Published on 26 Mar 2026 - 21:12

score 64 · Answer 13 · 2015-11-19 19:15:25

64

Views

Counting divisors of a number

Published on 19 Nov 2015 - 19:15

score 77 · Answer 14 · 2015-11-25 15:32:58

77

Views

With $s(n)=\sum_{k=1}^n n \bmod k$, can be justified that $\forall\epsilon>0$ let us $\lim_{n\to\infty}\frac{s(n-1)}{\epsilon+s(n)}=1?$

Published on 25 Nov 2015 - 15:32

score 75 · Answer 15 · 2015-11-25 22:46:46

75

Views

Arithmetic functions & logs

Published on 25 Nov 2015 - 22:46

List Question

Looking an asymptotic for $\sum_{k\leq x}\Lambda(k)e^k$, where $\Lambda (n)$ is the von Mangoldt function

LCM of binomial coefficients and related functions

Number of zeros of a polynomial modulo n is a multiplicative function

On Abel summation $\sum_{e<n\leq x}\left(\mu(n)\cdot\int_2^n\frac{ds}{\log s}\right)$, where $\mu(n)$ is the Möbius function

Arithmetic Derivative

Formula with $\sigma(n)$ and $\phi(n)$ is not an integer if $n$ is not square-free

The sum $\sum_{n\leq x}\sum_{\substack{1\leq k\leq n \\ gdc(k,n)=1}}\cos^2\pi \frac{k}{n}$ diverges as $x$, when $x$ tends to infitity

On $\sigma(n)<n+\frac{n}{2}\log\frac{n+1}{n-1}+\frac{n}{4} \left(\sum_{\substack{d|n,1<d<n}}\log\frac{(n+d)(n+1)}{(n-d)(n-1)}\right)$

Numbers $n$ whose prime factors are $2$ and $5$ if and only if $\sum_{k=1}^{rad(n)}\mu(k)k=0$?

Show that if $n$ is even then $\sum_{d|n}\mu(d)\phi(d)=0$ using only Dirichlet Convolution propertys (without multiplicative function concepts)

Infinite sum of a function $g(n)=\sum_{d|n \; d\ne n}g(d)$

Using Dirichlet convolution where f = μ ∗ μ (Mobius) to find f(24)?

Counting divisors of a number

With $s(n)=\sum_{k=1}^n n \bmod k$, can be justified that $\forall\epsilon>0$ let us $\lim_{n\to\infty}\frac{s(n-1)}{\epsilon+s(n)}=1?$

Arithmetic functions & logs

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