Question

What are the patterns in the number of divisors $d(n)$ of the highly composite numbers?

score 594 · Answer 1 · 2014-07-21 22:47:08

594

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What are the patterns in the number of divisors $d(n)$ of the highly composite numbers?

Published on 21 Jul 2014 - 22:47

score 191 · Answer 2 · 2014-08-22 18:25:20

191

Views

Show that sum of divisors of a composite number $n$ is $> n+ \sqrt{n}$

Published on 22 Aug 2014 - 18:25

score 1.4k · Answer 3 · 2014-08-23 14:21:46

1.4k

Views

Why are multiples of abundant numbers also abundant numbers?

Published on 23 Aug 2014 - 14:21

score 186 · Answer 4 · 2014-08-24 22:54:18

186

Views

Find a closed form for the constant term

Published on 24 Aug 2014 - 22:54

score 2.7k · Answer 5 · 2026-03-25 09:32:09

2.7k

Views

For any positive integer $n$, show that $\sum_{d|n}\sigma(d) = \sum_{d|n}(n/d)\tau(d)$

Published on 25 Mar 2026 - 9:32

score 2.1k · Answer 6 · 2026-03-25 09:27:09

2.1k

Views

Prove that $\sum \limits_{d|n}(n/d)\sigma(d) = \sum \limits_{d|n}d\tau(d)$

Published on 25 Mar 2026 - 9:27

score 95 · Answer 7 · 2014-09-05 14:54:22

95

Views

With odd $\ n>9, \sigma(n) < {11\over 16} e^{\gamma} n \log \log n $?

Published on 05 Sep 2014 - 14:54

score 1.3k · Answer 8 · 2014-09-06 23:22:19

1.3k

Views

Could you give a definition of what is a superior highly composite number using only words?

Published on 06 Sep 2014 - 23:22

score 119 · Answer 9 · 2026-03-25 16:01:27

119

Views

If Lagarias' inequality is wrong, are there infinitely many counterexamples to it?

Published on 25 Mar 2026 - 16:01

score 94 · Answer 10 · 2026-03-25 10:58:54

94

Views

Who should I ask for Robin's paper? At any rate, I want to find out if a similar result to his can be achieved with 36 instead of 12.

Published on 25 Mar 2026 - 10:58

score 114 · Answer 11 · 2026-03-25 17:33:19

114

Views

Number of divisiors of $n$ less than $m$

Published on 25 Mar 2026 - 17:33

score 63 · Answer 12 · 2026-03-25 09:47:00

63

Views

Why is this Moebius equivalence true?

Published on 25 Mar 2026 - 9:47

score 165 · Answer 13 · 2026-03-25 14:18:22

165

Views

About the 'sigma' function.

Published on 25 Mar 2026 - 14:18

score 784 · Answer 14 · 2014-10-20 13:46:28

784

Views

how to sum the divisors of N mod K if all I have is N mod K?

Published on 20 Oct 2014 - 13:46

score 3.1k · Answer 15 · 2014-10-28 04:22:33

3.1k

Views

What's wrong in this proof of $10$ is a solitary number?

Published on 28 Oct 2014 - 4:22

List Question

What are the patterns in the number of divisors $d(n)$ of the highly composite numbers?

Show that sum of divisors of a composite number $n$ is $> n+ \sqrt{n}$

Why are multiples of abundant numbers also abundant numbers?

Find a closed form for the constant term

For any positive integer $n$, show that $\sum_{d|n}\sigma(d) = \sum_{d|n}(n/d)\tau(d)$

Prove that $\sum \limits_{d|n}(n/d)\sigma(d) = \sum \limits_{d|n}d\tau(d)$

With odd $\ n>9, \sigma(n) < {11\over 16} e^{\gamma} n \log \log n $?

Could you give a definition of what is a superior highly composite number using only words?

If Lagarias' inequality is wrong, are there infinitely many counterexamples to it?

Who should I ask for Robin's paper? At any rate, I want to find out if a similar result to his can be achieved with 36 instead of 12.

Number of divisiors of $n$ less than $m$

Why is this Moebius equivalence true?

About the 'sigma' function.

how to sum the divisors of N mod K if all I have is N mod K?

What's wrong in this proof of $10$ is a solitary number?

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