List questions from divisor-sum

Published on 28 Oct 2016 - 14:21

727

Views

Sum of divisors is power of 2, is n square-free?

Published on 03 Nov 2016 - 16:48

142

Views

Sum of Powers of Euler's Totient Function.

Published on 28 Mar 2026 - 2:49

118

Views

What is the closed form of :$\sum_{n=2}^{\infty }\frac{\tau(2^n-1)}{\phi(2^n-1)}$?

Published on 07 Nov 2016 - 21:08

65

Views

Which of these two expressions (related to primes) is greater: $\frac{\sigma{(n)}}{n}$ or $\sum_{p \le n}{\frac{1}{p}}$?

Published on 25 Mar 2026 - 17:42

65

Views

Help with a theorem of Ramanujan

Published on 16 Nov 2016 - 18:30

195

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Has anyone seen this divisor function identity?

Published on 25 Mar 2026 - 20:34

156

Views

On a new identity involving the sum of remainders function

Published on 18 Nov 2016 - 23:48

31

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Is this true for $n \geq 1:\sigma(4^n) \bmod 4=3$ and how do i show it if it is?

Published on 26 Nov 2016 - 20:59

143

Views

Closed form for $\sum\limits_{d|n}\sigma(d)$?

Published on 25 Mar 2026 - 15:58

370

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What is the asymptotic density of deficient-perfect numbers?

Published on 26 Mar 2026 - 9:17

170

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Sum of number of divisors for square n

Published on 22 Dec 2016 - 3:15

83

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How do I solve this: $\sigma(n)=\frac{3n(n-1)}{2}$?

Published on 27 Dec 2016 - 14:03

153

Views

When is $\displaystyle \phi(\sigma(n)) $ is a perfect square?

Published on 25 Mar 2026 - 17:38

226

Views

Property of 2016

Published on 02 Jan 2017 - 9:55

List Question

What's the sum of all the positive integral divisors of $540$?

Sum of divisors is power of 2, is n square-free?

Sum of Powers of Euler's Totient Function.

What is the closed form of :$\sum_{n=2}^{\infty }\frac{\tau(2^n-1)}{\phi(2^n-1)}$?

Which of these two expressions (related to primes) is greater: $\frac{\sigma{(n)}}{n}$ or $\sum_{p \le n}{\frac{1}{p}}$?

Help with a theorem of Ramanujan

Has anyone seen this divisor function identity?

On a new identity involving the sum of remainders function

Is this true for $n \geq 1:\sigma(4^n) \bmod 4=3$ and how do i show it if it is?

Closed form for $\sum\limits_{d|n}\sigma(d)$?

What is the asymptotic density of deficient-perfect numbers?

Sum of number of divisors for square n

How do I solve this: $\sigma(n)=\frac{3n(n-1)}{2}$?

When is $\displaystyle \phi(\sigma(n)) $ is a perfect square?

Property of 2016

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