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Combining a working hypothesis for odd perfect numbers with an inequality for logarithms

score 78 · Answer 1 · 2016-07-15 20:29:32

78

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Combining a working hypothesis for odd perfect numbers with an inequality for logarithms

Published on 15 Jul 2016 - 20:29

score 83 · Answer 2 · 2016-07-19 14:43:38

83

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If $N = q^k n^2$ is an odd perfect number with Euler prime $q$, and $k=1$, does it follow that $\frac{\sigma(n^2)}{n^2} \geq 2 - \frac{5}{3q}$?

Published on 19 Jul 2016 - 14:43

score 71 · Answer 3 · 2016-07-21 07:43:06

71

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Notice that the sum of the powers of $2$ from $1$, which is $2^0$, to $2^{n-1}$ is equal to ${2^n}{-1}$.

Published on 21 Jul 2016 - 7:43

score 67 · Answer 4 · 2016-07-28 04:10:23

67

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the sum of eight three digit consequtive even numbers is S.When Sis divided by 5,it results in a perfect cube

Published on 28 Jul 2016 - 4:10

score 78 · Answer 5 · 2016-08-31 10:18:04

78

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Is the following statement true if $N = q^k n^2$ is an odd perfect number given in Eulerian form?

Published on 31 Aug 2016 - 10:18

score 82 · Answer 6 · 2016-09-05 21:07:14

82

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On identities and congruences involving the harmonic mean of odd perfect numbers

Published on 05 Sep 2016 - 21:07

score 157 · Answer 7 · 2016-09-08 04:09:34

157

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On a conjectured relationship between the least prime factor and the Euler prime of an odd perfect number

Published on 08 Sep 2016 - 4:09

score 67 · Answer 8 · 2016-09-12 09:35:56

67

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If $N = q^k n^2$ is an odd perfect number with Euler prime $q$, does the following implication hold?

Published on 12 Sep 2016 - 9:35

score 399 · Answer 9 · 2016-09-14 16:36:03

399

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On the undecidability of the existence of odd perfect numbers

Published on 14 Sep 2016 - 16:36

score 332 · Answer 10 · 2016-09-21 20:21:11

332

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Can a multi-perfect number be a perfect square?

Published on 21 Sep 2016 - 20:21

score 294 · Answer 11 · 2026-03-25 06:30:31

294

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Explain these concepts of String Theory in easy words for mathematicians, from a popular point of view

Published on 25 Mar 2026 - 6:30

score 173 · Answer 12 · 2016-09-24 17:47:39

173

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If $q^k n^2$ is an odd perfect number with Euler prime $q$, can $q=17$ hold?

Published on 24 Sep 2016 - 17:47

score 608 · Answer 13 · 2026-03-25 16:00:14

608

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Why are non-trivial powers called perfect powers?

Published on 25 Mar 2026 - 16:00

score 56 · Answer 14 · 2016-10-28 17:44:00

56

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There are at most finitely many primes not dividing any elements in this sequence

Published on 28 Oct 2016 - 17:44

score 613 · Answer 15 · 2016-11-03 05:09:26

613

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Prove that if $2^a$ is superperfect, then $2^{a+1} - 1$ is a Mersenne prime.

Published on 03 Nov 2016 - 5:09

List Question

Combining a working hypothesis for odd perfect numbers with an inequality for logarithms

If $N = q^k n^2$ is an odd perfect number with Euler prime $q$, and $k=1$, does it follow that $\frac{\sigma(n^2)}{n^2} \geq 2 - \frac{5}{3q}$?

Notice that the sum of the powers of $2$ from $1$, which is $2^0$, to $2^{n-1}$ is equal to ${2^n}{-1}$.

the sum of eight three digit consequtive even numbers is S.When Sis divided by 5,it results in a perfect cube

Is the following statement true if $N = q^k n^2$ is an odd perfect number given in Eulerian form?

On identities and congruences involving the harmonic mean of odd perfect numbers

On a conjectured relationship between the least prime factor and the Euler prime of an odd perfect number

If $N = q^k n^2$ is an odd perfect number with Euler prime $q$, does the following implication hold?

On the undecidability of the existence of odd perfect numbers

Can a multi-perfect number be a perfect square?

Explain these concepts of String Theory in easy words for mathematicians, from a popular point of view

If $q^k n^2$ is an odd perfect number with Euler prime $q$, can $q=17$ hold?

Why are non-trivial powers called perfect powers?

There are at most finitely many primes not dividing any elements in this sequence

Prove that if $2^a$ is superperfect, then $2^{a+1} - 1$ is a Mersenne prime.

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