List questions from divisor-sum

Published on 02 May 2017 - 19:34

515

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Why are these number pairs not Amicable Numbers?

Published on 03 May 2017 - 10:11

193

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The integer values of $\sum_{d|n}\frac{\sigma(n/d)^d}{d}$.

Published on 30 Mar 2026 - 8:23

418

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Interesting convergence in divisor sums up to $10^k$

Published on 15 May 2017 - 4:05

121

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On odd integers $n\geq 1$ that satisfy $2n\varphi(\sigma(n))=\sigma(n)\varphi(n)$

Published on 18 May 2017 - 10:19

45

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If $N=q^k n^2$ is an odd perfect number, which is bigger, $\sigma(n^2)/n^2$ or $\sigma(n)/q^k$?

Published on 27 Mar 2026 - 3:59

335

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Finding the inverse of divisor functions in terms of $\mu$

Published on 07 Jun 2017 - 10:37

127

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A question on the Euler prime of odd perfect numbers

Published on 27 Mar 2026 - 3:58

92

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How often does $D(n^2) = m^2$ happen, where $D(x)$ is the deficiency of $x$?

Published on 28 Mar 2026 - 3:27

161

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Do there exist deficient-perfect square numbers whose deficiency is also a square (and not one)?

Published on 28 Mar 2026 - 1:46

134

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First step with the equation $\sigma(n)=\phi(n)+\operatorname{rad}(n)$: a first statement

Published on 28 Mar 2026 - 1:48

1.1k

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Calculating $\sum \sigma (n)$

Published on 01 Jul 2017 - 1:05

155

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Dirichlet Sum over number of Divisors

Published on 02 Jul 2017 - 7:34

80

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Is there a limit to the sum of non-trivial factors of N divided by N

Published on 03 Jul 2017 - 14:19

137

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Upper Bound on Aliquot Sequence

Published on 03 Jul 2017 - 19:54

List Question

Closed form for $\sum_{k=1}^n \sigma(k^2)$

Why are these number pairs not Amicable Numbers?

The integer values of $\sum_{d|n}\frac{\sigma(n/d)^d}{d}$.

Interesting convergence in divisor sums up to $10^k$

On odd integers $n\geq 1$ that satisfy $2n\varphi(\sigma(n))=\sigma(n)\varphi(n)$

If $N=q^k n^2$ is an odd perfect number, which is bigger, $\sigma(n^2)/n^2$ or $\sigma(n)/q^k$?

Finding the inverse of divisor functions in terms of $\mu$

A question on the Euler prime of odd perfect numbers

How often does $D(n^2) = m^2$ happen, where $D(x)$ is the deficiency of $x$?

Do there exist deficient-perfect square numbers whose deficiency is also a square (and not one)?

First step with the equation $\sigma(n)=\phi(n)+\operatorname{rad}(n)$: a first statement

Calculating $\sum \sigma (n)$

Dirichlet Sum over number of Divisors

Is there a limit to the sum of non-trivial factors of N divided by N

Upper Bound on Aliquot Sequence

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