List questions from divisor-sum

Published on 10 Apr 2026 - 6:17

1.5k

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

Published on 14 Apr 2026 - 17:25

1k

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

Published on 15 Apr 2026 - 7:08

120

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What is known about iterative behavior of this function?

Published on 10 Apr 2026 - 15:48

279

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Can the difference between consecutive even abundant numbers exceed 6?

Published on 09 Apr 2026 - 13:03

94

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Inquiry about the Wolfram MathWorld entry on Odd Perfect Number

Published on 14 Apr 2026 - 17:16

75

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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 10 May 2026 - 14:32

78

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

Published on 14 Apr 2026 - 22:25

90

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On a theorem of Zumkeller related to twin primes

Published on 10 May 2026 - 15:09

120

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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 10 May 2026 - 14:32

143

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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 10 May 2026 - 14:32

81

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

Published on 16 Apr 2026 - 10:58

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 16 Apr 2026 - 3:34

107

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

Published on 10 May 2026 - 14:30

166

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Could a Fermat prime divide an odd perfect number?

Published on 10 May 2026 - 14:30

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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