List questions from divisor-sum

Published on 14 Sep 2017 - 12:23

132

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Show that $\sigma(n)$ is equally often even and odd

Published on 26 Mar 2026 - 0:52

1.4k

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"I am sure there are infinitely many perfect numbers"

Published on 27 Mar 2026 - 3:58

186

Views

Are there infinitely many different primes of the form $\sigma(n^2)-\varphi(n)\sigma(n)$?

Published on 25 Sep 2017 - 14:19

49

Views

If $p$ is prime, $m$ is composite and deficient, and $I(p) < I(m)$, does it follow that $m < p$, where $I(x)=\sigma(x)/x$ for $x \in \mathbb{N}$?

Published on 28 Sep 2017 - 23:09

160

Views

Sum of a floor function

Published on 07 Oct 2017 - 16:21

112

Views

Why is this sequence not in the Online Encyclopedia of Integer Sequences?

Published on 08 Oct 2017 - 6:15

80

Views

Upper and lower density of the set of natural numbers whose sum of positive divisors is a perfect square

Published on 28 Mar 2026 - 3:27

109

Views

On puzzles about $\pi$erfect numbers: has $\sigma(\pi(n))=\pi(2n)$ infinitely many solutions?

Published on 17 Oct 2017 - 12:10

40

Views

What does $[m](T)$ mean in the context of algebraic curve divisors?

Published on 18 Oct 2017 - 0:45

1.1k

Views

Sum of perfect square divisors

Published on 24 Oct 2017 - 13:17

86

Views

Is there an efficient algorithm to decide whether a number is pseudoperfect?

Published on 25 Oct 2017 - 10:50

55

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Mods and Multiplicative functions

Published on 26 Mar 2026 - 12:51

82

Views

Show that the quotient $\frac{\sigma(p^3)}{\tau(p^3)}$ is an integer for $p$ prime

Published on 26 Mar 2026 - 11:00

134

Views

Combinatorial Interpretation of the Sum-of-Divisor Function?

Published on 28 Oct 2017 - 8:15

List Question

Calculating divisors for generative music sequence

Show that $\sigma(n)$ is equally often even and odd

"I am sure there are infinitely many perfect numbers"

Are there infinitely many different primes of the form $\sigma(n^2)-\varphi(n)\sigma(n)$?

If $p$ is prime, $m$ is composite and deficient, and $I(p) < I(m)$, does it follow that $m < p$, where $I(x)=\sigma(x)/x$ for $x \in \mathbb{N}$?

Sum of a floor function

Why is this sequence not in the Online Encyclopedia of Integer Sequences?

Upper and lower density of the set of natural numbers whose sum of positive divisors is a perfect square

On puzzles about $\pi$erfect numbers: has $\sigma(\pi(n))=\pi(2n)$ infinitely many solutions?

What does $[m](T)$ mean in the context of algebraic curve divisors?

Sum of perfect square divisors

Is there an efficient algorithm to decide whether a number is pseudoperfect?

Mods and Multiplicative functions

Show that the quotient $\frac{\sigma(p^3)}{\tau(p^3)}$ is an integer for $p$ prime

Combinatorial Interpretation of the Sum-of-Divisor Function?

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