Question

Prove that if $2^{p}-1$ is prime then $n=2^{p-1}(2^p-1)$ is a perfect number

score 6k · Answer 1 · 2026-04-17 03:45:10

6k

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Prove that if $2^{p}-1$ is prime then $n=2^{p-1}(2^p-1)$ is a perfect number

Published on 17 Apr 2026 - 3:45

score 155 · Answer 2 · 2026-05-10 18:03:25

155

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What do we know about Sorli's Conjecture and Odd Perfect Numbers?

Published on 10 May 2026 - 18:03

score 109 · Answer 3 · 2026-04-16 12:45:21

109

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How I could transform this into product over primes :$s_p$= $\frac{1}{2^2-1}+\frac{1}{2^3-1}+....\frac{1}{2^p-1}$?

Published on 16 Apr 2026 - 12:45

score 210 · Answer 4 · 2026-05-10 16:57:15

210

Views

On the indivisibility of odd perfect numbers by small numbers

Published on 10 May 2026 - 16:57

score 1.3k · Answer 5 · 2026-04-14 11:02:53

1.3k

Views

Is this proof that there are no perfect, odd, integer square numbers legitimate?

Published on 14 Apr 2026 - 11:02

score 426 · Answer 6 · 2026-04-17 02:13:44

426

Views

Why does not the perfect number formula imply there are infinitely many perfect numbers?

Published on 17 Apr 2026 - 2:13

score 1.1k · Answer 7 · 2026-04-15 17:39:26

1.1k

Views

Show that if $p$ is an odd prime, show a power $p^k$ can never be a perfect number

Published on 15 Apr 2026 - 17:39

score 116 · Answer 8 · 2026-04-15 07:27:51

116

Views

Show that the product of the divisors of an even perfect number is $n^p$.

Published on 15 Apr 2026 - 7:27

score 143 · Answer 9 · 2026-05-10 18:59:44

143

Views

Improving the bound $q < n\sqrt{3}$ for an odd perfect number $N = {q^k}{n^2}$ given in Eulerian form

Published on 10 May 2026 - 18:59

score 70 · Answer 10 · 2026-04-14 11:39:14

70

Views

On a certain "obvious" implication concerning odd perfect numbers

Published on 14 Apr 2026 - 11:39

score 215 · Answer 11 · 2026-04-11 00:28:04

215

Views

Finding Perfect numbers which are sum of consecutive prime number.

Published on 11 Apr 2026 - 0:28

score 84 · Answer 12 · 2026-04-17 04:06:51

84

Views

If $q^k n^2$ is an odd perfect number with special prime $q$, is it true that $\sigma(n^2)/q^k \mid n^2$?

Published on 17 Apr 2026 - 4:06

score 103 · Answer 13 · 2026-03-25 21:54:06

103

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If $q^k n^2$ is an odd perfect number with special prime $q$, then can $n^2 - q^k$ be a cube?

Published on 25 Mar 2026 - 21:54

score 490 · Answer 14 · 2026-04-12 23:58:43

490

Views

Relations between composite numbers, prime numbers, and perfect numbers.

Published on 12 Apr 2026 - 23:58

score 179 · Answer 15 · 2026-04-10 17:01:35

179

Views

Number in binary as a product

Published on 10 Apr 2026 - 17:01

List Question

Prove that if $2^{p}-1$ is prime then $n=2^{p-1}(2^p-1)$ is a perfect number

What do we know about Sorli's Conjecture and Odd Perfect Numbers?

How I could transform this into product over primes :$s_p$= $\frac{1}{2^2-1}+\frac{1}{2^3-1}+....\frac{1}{2^p-1}$?

On the indivisibility of odd perfect numbers by small numbers

Is this proof that there are no perfect, odd, integer square numbers legitimate?

Why does not the perfect number formula imply there are infinitely many perfect numbers?

Show that if $p$ is an odd prime, show a power $p^k$ can never be a perfect number

Show that the product of the divisors of an even perfect number is $n^p$.

Improving the bound $q < n\sqrt{3}$ for an odd perfect number $N = {q^k}{n^2}$ given in Eulerian form

On a certain "obvious" implication concerning odd perfect numbers

Finding Perfect numbers which are sum of consecutive prime number.

If $q^k n^2$ is an odd perfect number with special prime $q$, is it true that $\sigma(n^2)/q^k \mid n^2$?

If $q^k n^2$ is an odd perfect number with special prime $q$, then can $n^2 - q^k$ be a cube?

Relations between composite numbers, prime numbers, and perfect numbers.

Number in binary as a product

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