Question

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

score 84 · Answer 1 · 2026-03-26 07:35:22

84

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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 26 Mar 2026 - 7:35

score 206 · Answer 2 · 2016-07-20 10:04:53

206

Views

Conjecture: Every prime number is the difference between a prime number and a power of $2$

Published on 20 Jul 2016 - 10:04

score 57 · Answer 3 · 2016-07-22 19:39:13

57

Views

For each prime $p>3$ there are non twin primes $q,r$ with $p^3=2q+r$

Published on 22 Jul 2016 - 19:39

score 119 · Answer 4 · 2026-03-25 12:49:47

119

Views

Even natural numbers are sums of two primes with twins or of two primes without twins

Published on 25 Mar 2026 - 12:49

score 336 · Answer 5 · 2026-03-25 06:05:41

336

Views

If $|G|=p^3q^2$ then $\Phi(G)$ is cyclic for primes $p\neq q$.

Published on 25 Mar 2026 - 6:05

score 105 · Answer 6 · 2016-07-28 18:21:43

105

Views

Any even $n> 10$ can be written as $n = pp'+p''$ for some primes $p,p',p''$

Published on 28 Jul 2016 - 18:21

score 328 · Answer 7 · 2016-07-30 13:16:31

328

Views

Conjectured Compositeness Test for $E_n(b)=\frac{b^{2^n}+1}{2}$

Published on 30 Jul 2016 - 13:16

score 71 · Answer 8 · 2016-08-02 06:43:39

71

Views

The relationship between the order of an element in a group and the order of its image

Published on 02 Aug 2016 - 6:43

score 1.5k · Answer 9 · 2016-08-04 19:02:20

1.5k

Views

Every prime number divide some sum of the first $k$ primes.

Published on 04 Aug 2016 - 19:02

score 408 · Answer 10 · 2026-03-25 14:27:12

408

Views

About the distribution of Gaussian prime pairs

Published on 25 Mar 2026 - 14:27

score 1.2k · Answer 11 · 2026-03-25 23:10:44

1.2k

Views

Simplified variant of Collatz conjecture.

Published on 25 Mar 2026 - 23:10

score 157 · Answer 12 · 2016-08-09 21:34:29

157

Views

Counting even and odd numbers in the columns of a triangular arrangement of the integers

Published on 09 Aug 2016 - 21:34

score 219 · Answer 13 · 2026-03-25 21:44:44

219

Views

Primes Between Triangular numbers and Legendre's Conjecture. Reference request

Published on 25 Mar 2026 - 21:44

score 133 · Answer 14 · 2016-08-11 21:20:13

133

Views

Counting multiple of $3$ in a triangular arrangement of the integers.

Published on 11 Aug 2016 - 21:20

score 252 · Answer 15 · 2016-08-12 15:32:48

252

Views

Conjectured Compositeness Test for Generalized Fermat Numbers

Published on 12 Aug 2016 - 15:32

List Question

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

Conjecture: Every prime number is the difference between a prime number and a power of $2$

For each prime $p>3$ there are non twin primes $q,r$ with $p^3=2q+r$

Even natural numbers are sums of two primes with twins or of two primes without twins

If $|G|=p^3q^2$ then $\Phi(G)$ is cyclic for primes $p\neq q$.

Any even $n> 10$ can be written as $n = pp'+p''$ for some primes $p,p',p''$

Conjectured Compositeness Test for $E_n(b)=\frac{b^{2^n}+1}{2}$

The relationship between the order of an element in a group and the order of its image

Every prime number divide some sum of the first $k$ primes.

About the distribution of Gaussian prime pairs

Simplified variant of Collatz conjecture.

Counting even and odd numbers in the columns of a triangular arrangement of the integers

Primes Between Triangular numbers and Legendre's Conjecture. Reference request

Counting multiple of $3$ in a triangular arrangement of the integers.

Conjectured Compositeness Test for Generalized Fermat Numbers

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