List questions from divisor-sum

Published on 22 Mar 2026 - 16:12

1.5k

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Is $\phi(n) + \sigma(n) \geq 2n$ always true?

Published on 20 Aug 2018 - 14:59

1k

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Does there exist $a_0$, such that $\{a_n\}_{n=0}^{\infty}$ is unbounded?

Published on 21 Aug 2018 - 13:39

118

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What is known about iterative behavior of this function?

Published on 26 Aug 2018 - 15:08

277

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Can the difference between consecutive even abundant numbers exceed 6?

Published on 26 Aug 2018 - 18:38

92

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Inquiry about the Wolfram MathWorld entry on Odd Perfect Number

Published on 27 Aug 2018 - 9:17

71

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Are there any other squares $n^2$ for which $\gcd(n^2, \sigma(n^2)) = 2n^2 - \sigma(n^2)$?

Published on 04 Sep 2018 - 8:28

75

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Are there any $\ m\ $- superperfect numbers for $\ \ m>2\ \ $?

Published on 04 Sep 2018 - 21:32

86

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On a theorem of Zumkeller related to twin primes

Published on 09 Sep 2018 - 10:30

116

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Is $(q^k n^2 \text{ is perfect }) \iff (D(q^k)D(n^2) = 2s(q^k)s(n^2))$ only true for odd perfect numbers $q^k n^2$?

Published on 02 Oct 2018 - 7:44

141

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What is the common (and simplified) value for $D(q^k)D(n^2) = 2s(q^k)s(n^2)$ when $q^k n^2$ is an odd perfect number?

Published on 02 Oct 2018 - 11:26

78

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Is it always true that if $\sigma(n) + 1$ is divisible by $n$ then $\sigma(n) = 2n - 1$?

Published on 06 Oct 2018 - 14:28

1.1k

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Asymptotic formula for $\sum_{n\leq x}\sigma(n)$ knowing $\sum_{n\leq x}\frac{\sigma(n)}{n}$

Published on 13 Oct 2018 - 17:54

103

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Does mathlove's answer imply that $D(n^2) \mid n^2$?

Published on 18 Oct 2018 - 11:53

162

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Could a Fermat prime divide an odd perfect number?

Published on 18 Oct 2018 - 15:09

List Question

Question about a result on odd perfect numbers

Is $\phi(n) + \sigma(n) \geq 2n$ always true?

Does there exist $a_0$, such that $\{a_n\}_{n=0}^{\infty}$ is unbounded?

What is known about iterative behavior of this function?

Can the difference between consecutive even abundant numbers exceed 6?

Inquiry about the Wolfram MathWorld entry on Odd Perfect Number

Are there any other squares $n^2$ for which $\gcd(n^2, \sigma(n^2)) = 2n^2 - \sigma(n^2)$?

Are there any $\ m\ $- superperfect numbers for $\ \ m>2\ \ $?

On a theorem of Zumkeller related to twin primes

Is $(q^k n^2 \text{ is perfect }) \iff (D(q^k)D(n^2) = 2s(q^k)s(n^2))$ only true for odd perfect numbers $q^k n^2$?

What is the common (and simplified) value for $D(q^k)D(n^2) = 2s(q^k)s(n^2)$ when $q^k n^2$ is an odd perfect number?

Is it always true that if $\sigma(n) + 1$ is divisible by $n$ then $\sigma(n) = 2n - 1$?

Asymptotic formula for $\sum_{n\leq x}\sigma(n)$ knowing $\sum_{n\leq x}\frac{\sigma(n)}{n}$

Does mathlove's answer imply that $D(n^2) \mid n^2$?

Could a Fermat prime divide an odd perfect number?

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