List questions from divisor-counting-function

Published on 06 Mar 2016 - 15:46

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Possible divisors of $s(2s+1)$

Published on 16 Mar 2016 - 20:24

129

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Possible divisors of $s(2s+1)$ follow up question.

Published on 17 Mar 2016 - 17:27

128

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Has limit $\frac{\sigma_0(n)\sigma_2(n)}{(\sigma(n))^2H_n},$ where $H_n$ is the nth harmonic number?

Published on 21 Mar 2016 - 15:01

350

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Sum of number-of-divisors function equals $\sum_{j=1}^{n} \lfloor n/j \rfloor$.

Published on 19 Apr 2016 - 5:43

73

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On those integers $n>1$ such that there exists a commutative ring with identity with exactly $n$ ideals

Published on 29 Apr 2016 - 14:40

3.4k

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Compute the Euler function $\phi(n)$ for $n = 360$ as well as the number of divisors $d(n)$.

Published on 20 May 2016 - 9:11

252

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Number of solutions to this nice equation $\varphi(n)+\tau(n^2)=n$

Published on 25 Jun 2016 - 5:12

582

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Number theory Exercise: $\sum_{d \mid n} \mu(d) d(d) = (-1)^{\omega(n)}$ and $\sum_{d \mid n} \mu(d) \sigma (d)$

Published on 04 Apr 2013 - 11:49

1.6k

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Arithmetical Functions Sum, $\sum\limits_{d|n}\sigma(d)\phi(\frac{n}{d})$ and $\sum\limits_{d|n}\tau(d)\phi(\frac{n}{d})$

Published on 28 Aug 2013 - 7:08

18.5k

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Smallest number with specific number of divisors

Published on 17 Sep 2013 - 15:28

786

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Prove that $\tau(2^n-1) \geq \tau(n)$ for all positive integers $n$.

Published on 24 Sep 2013 - 11:58

156

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Product of all divisors

Published on 21 Oct 2013 - 6:00

318

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Prime factorization, distinct primes

Published on 01 Nov 2013 - 14:45

48

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Finding $m∈\mathbb N$ such that $d^n(m)$ is not a perfect square for any $n\geq1$

Published on 04 Nov 2013 - 5:19

List Question

find number of positive integers smaller $N$ that have an even number of proper divisors

Possible divisors of $s(2s+1)$

Possible divisors of $s(2s+1)$ follow up question.

Has limit $\frac{\sigma_0(n)\sigma_2(n)}{(\sigma(n))^2H_n},$ where $H_n$ is the nth harmonic number?

Sum of number-of-divisors function equals $\sum_{j=1}^{n} \lfloor n/j \rfloor$.

On those integers $n>1$ such that there exists a commutative ring with identity with exactly $n$ ideals

Compute the Euler function $\phi(n)$ for $n = 360$ as well as the number of divisors $d(n)$.

Number of solutions to this nice equation $\varphi(n)+\tau(n^2)=n$

Number theory Exercise: $\sum_{d \mid n} \mu(d) d(d) = (-1)^{\omega(n)}$ and $\sum_{d \mid n} \mu(d) \sigma (d)$

Arithmetical Functions Sum, $\sum\limits_{d|n}\sigma(d)\phi(\frac{n}{d})$ and $\sum\limits_{d|n}\tau(d)\phi(\frac{n}{d})$

Smallest number with specific number of divisors

Prove that $\tau(2^n-1) \geq \tau(n)$ for all positive integers $n$.

Product of all divisors

Prime factorization, distinct primes

Finding $m∈\mathbb N$ such that $d^n(m)$ is not a perfect square for any $n\geq1$

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