List questions from divisor-counting-function

Published on 27 Mar 2026 - 7:50

102

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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 25 Mar 2026 - 7:45

39

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

Published on 10 May 2026 - 19:03

538

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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 Mar 2026 - 7:46

180

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

Published on 25 Mar 2026 - 11:13

255

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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 25 Mar 2026 - 7:46

180

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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 25 Mar 2026 - 7:46

264

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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 25 Mar 2026 - 7:46

99

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

Published on 25 Mar 2026 - 7:43

84

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Alternate method to derive the following equation

Published on 25 Mar 2026 - 7:42

516

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Finding the summation of the floor of the series identity

Published on 25 Mar 2026 - 7:44

262

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

Published on 09 Apr 2026 - 8:08

373

Views

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

Published on 25 Mar 2026 - 7:40

847

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

Published on 10 May 2026 - 19:10

994

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

Published on 25 Mar 2026 - 7:45

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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