List questions from divisor-counting-function

Published on 24 Jan 2019 - 15:55

101

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Prove that there exist infinitely many $n$ such that $d(n+1)>d(n)$, where $d(n)$ is number of positive factors

Published on 13 Mar 2019 - 16:59

34

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Show that $\sigma=c_1*c_1$, where $c_1$ is the constant function $1$.

Published on 22 Mar 2026 - 8:01

537

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Let $d(n)$ be the number of positive divisors of $n$. Find all $n$ such that $\frac{n}{d(n)}$ is prime.

Published on 25 Apr 2019 - 16:07

179

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For every sufficiently large $m$ there exists $k$ such that $m = k + \tau(k)$

Published on 03 Jun 2019 - 13:39

254

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Behavior of integer recurrence $u_0\geq 2$, $u_{n+1}=d(u_n)^\alpha$, for $\alpha \geq 3$, where $d$ is the number-of-divisors function

Published on 02 Aug 2019 - 19:34

179

Views

Does $-\frac{1}{2}+\frac{1}{3}-\frac{1}{5}+\frac{1}{7}+\frac{1}{11}+\frac{1}{13}+\frac{1}{17}+\frac{1}{19}+\frac{1}{23}+\dots$ converge?

Published on 03 Aug 2019 - 9:09

263

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Where does the identity $\tau(nm) = \sum_{d \mid (m, n)} \mu(d) \tau(n/d) \tau(m/d)$ come from?

Published on 31 Aug 2019 - 10:32

98

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Possible to identify a quadratic polynomial using only $\sigma_0(f(x))$?

Published on 13 Sep 2019 - 11:05

83

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Alternate method to derive the following equation

Published on 26 Sep 2019 - 15:23

515

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Finding the summation of the floor of the series identity

Published on 23 Mar 2026 - 1:54

261

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Sequences where each number is a divisor of one less than the next

Published on 17 Mar 2026 - 4:52

372

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Evaluating a sum with Mobius function $\sum_{d|n}\tau(d)\mu(d)$

Published on 22 Mar 2026 - 22:38

845

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Prove $\sum_{k\mid n}{\mu(k)d(k)}=(-1)^{\omega{(n)}}$

Published on 19 Jul 2014 - 18:19

993

Views

The number of divisors of any positive number $n$ is $\le 2\sqrt{n}$

Published on 23 Mar 2026 - 14:15

List Question

Number of Pythagorean Triples

Prove that there exist infinitely many $n$ such that $d(n+1)>d(n)$, where $d(n)$ is number of positive factors

Show that $\sigma=c_1*c_1$, where $c_1$ is the constant function $1$.

Let $d(n)$ be the number of positive divisors of $n$. Find all $n$ such that $\frac{n}{d(n)}$ is prime.

For every sufficiently large $m$ there exists $k$ such that $m = k + \tau(k)$

Behavior of integer recurrence $u_0\geq 2$, $u_{n+1}=d(u_n)^\alpha$, for $\alpha \geq 3$, where $d$ is the number-of-divisors function

Does $-\frac{1}{2}+\frac{1}{3}-\frac{1}{5}+\frac{1}{7}+\frac{1}{11}+\frac{1}{13}+\frac{1}{17}+\frac{1}{19}+\frac{1}{23}+\dots$ converge?

Where does the identity $\tau(nm) = \sum_{d \mid (m, n)} \mu(d) \tau(n/d) \tau(m/d)$ come from?

Possible to identify a quadratic polynomial using only $\sigma_0(f(x))$?

Alternate method to derive the following equation

Finding the summation of the floor of the series identity

Sequences where each number is a divisor of one less than the next

Evaluating a sum with Mobius function $\sum_{d|n}\tau(d)\mu(d)$

Prove $\sum_{k\mid n}{\mu(k)d(k)}=(-1)^{\omega{(n)}}$

The number of divisors of any positive number $n$ is $\le 2\sqrt{n}$

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