List questions from divisor-counting-function

Published on 02 Nov 2011 - 23:54

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Sum of Positive Divisors: $\sum_{d|n} \mu(n/d)\nu(d)=1$ and $\sum_{d|n} \mu(n/d)\sigma(d)=n$

Published on 28 Apr 2012 - 8:32

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Finding the divisors of the number $p^3q^6$

Published on 23 Jul 2012 - 2:57

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How to prove $ \prod_{d|n} d= n^{\frac{\tau (n)}{2}}$

Published on 21 Mar 2013 - 16:32

82

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How does the primality of $n$ impact the number of divisors of $2n+1$?

Published on 04 Aug 2020 - 14:28

125

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Limit superior of the number-of-divisors function $d(n)$

Published on 05 Aug 2020 - 8:51

184

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Inequality for divisor sigma $\sigma_{\nu}(n)$ function.

Published on 06 Sep 2020 - 16:10

103

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How do I prove ${\binom{n}{0}}+{\binom{n}{3}}+{\binom{n}{6}}+\cdots ={\frac{1}{3}}\left(2^{n}+2\cos {\frac{n\pi }{3}}\right)?$

Published on 14 Oct 2020 - 20:22

63

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What existing relationships are there in the divisor counting function for τ(m), τ(n) and τ(mn)?

Published on 17 Oct 2020 - 7:35

126

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Sum of recipocals of number of divisors

Published on 02 Nov 2020 - 20:50

43

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Proof of $ \sum_{q \le x/d} 1 = \frac{x}{d} + O(1) $

Published on 27 Dec 2020 - 15:19

56

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When is the number of Divisors of a Number equivalent to one of its Factors?

Published on 29 Dec 2020 - 18:30

92

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Finite Factors of Refactorable Numbers

Published on 31 Dec 2020 - 0:31

131

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About Euler totient function $\underbrace{\varphi( \varphi( \dots \varphi(}_{k\ \text{times}} n) \dots ))$

Published on 10 Feb 2021 - 12:35

51

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Trying to figure out the asymptotic density

Published on 11 Mar 2021 - 21:43

List Question

How to prove $\sum_{d|n} {\tau}^3(d)=\left(\sum_{d|n}{\tau}(d)\right)^2$

Sum of Positive Divisors: $\sum_{d|n} \mu(n/d)\nu(d)=1$ and $\sum_{d|n} \mu(n/d)\sigma(d)=n$

Finding the divisors of the number $p^3q^6$

How to prove $ \prod_{d|n} d= n^{\frac{\tau (n)}{2}}$

How does the primality of $n$ impact the number of divisors of $2n+1$?

Limit superior of the number-of-divisors function $d(n)$

Inequality for divisor sigma $\sigma_{\nu}(n)$ function.

How do I prove ${\binom{n}{0}}+{\binom{n}{3}}+{\binom{n}{6}}+\cdots ={\frac{1}{3}}\left(2^{n}+2\cos {\frac{n\pi }{3}}\right)?$

What existing relationships are there in the divisor counting function for τ(m), τ(n) and τ(mn)?

Sum of recipocals of number of divisors

Proof of $ \sum_{q \le x/d} 1 = \frac{x}{d} + O(1) $

When is the number of Divisors of a Number equivalent to one of its Factors?

Finite Factors of Refactorable Numbers

About Euler totient function $\underbrace{\varphi( \varphi( \dots \varphi(}_{k\ \text{times}} n) \dots ))$

Trying to figure out the asymptotic density

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