Question

If $\sigma(n) = 2n - d$ and $d \mid n$, is it true that $d = \gcd(n,\sigma(n))$?

score 46 · Answer 1 · 2026-03-25 07:53:19

46

Views

If $\sigma(n) = 2n - d$ and $d \mid n$, is it true that $d = \gcd(n,\sigma(n))$?

Published on 25 Mar 2026 - 7:53

score 47 · Answer 2 · 2019-01-29 06:46:24

47

Views

Improving the bound for $\sigma(q^k)/q^k$ where $q^k n^2$ is an odd perfect number given in Eulerian form

Published on 29 Jan 2019 - 6:46

score 98 · Answer 3 · 2019-01-29 15:56:11

98

Views

Either $np$ is even, or $n^2 − p^2$ is a multiple of $8$.

Published on 29 Jan 2019 - 15:56

score 139 · Answer 4 · 2019-02-01 09:53:12

139

Views

Can these bounds in terms of the abundancy index and deficiency functions be improved for deficient-perfect numbers?

Published on 01 Feb 2019 - 9:53

score 75 · Answer 5 · 2019-02-06 09:50:28

75

Views

A consequence of assuming the Descartes-Frenicle-Sorli Conjecture on odd perfect numbers

Published on 06 Feb 2019 - 9:50

score 159 · Answer 6 · 2026-03-25 07:52:27

159

Views

If $\sigma(n)/n = 5/3$, then $5 \nmid n$. Does it also follow that $3 \nmid \sigma(n)$?

Published on 25 Mar 2026 - 7:52

score 153 · Answer 7 · 2026-03-25 07:48:00

153

Views

On the golden ratio and odd perfect numbers

Published on 25 Mar 2026 - 7:48

score 37 · Answer 8 · 2019-02-27 10:00:58

37

Views

What is $\sigma(q^k)$ in terms of $k$ if $q \equiv 5 \pmod 8$?

Published on 27 Feb 2019 - 10:00

score 121 · Answer 9 · 2019-03-01 21:10:26

121

Views

On GCDs and odd perfect numbers

Published on 01 Mar 2019 - 21:10

score 124 · Answer 10 · 2026-03-25 07:53:26

124

Views

Breaking the barriers at $q=5$ and $q=13$ for $q^k n^2$ an odd perfect number with special prime $q$

Published on 25 Mar 2026 - 7:53

score 47 · Answer 11 · 2019-03-20 18:00:27

47

Views

Is this $\zeta(p)=\sum_{k\geq1 ,p\in \mathbb{P}}\frac{1}{{\sigma}_k(p)-1}$ true with sigma is power of sum divisor function?

Published on 20 Mar 2019 - 18:00

score 1k · Answer 12 · 2019-03-24 06:18:18

1k

Views

Sum of all positive divisors are prime

Published on 24 Mar 2019 - 6:18

score 798 · Answer 13 · 2019-03-29 05:08:08

798

Views

Finding the sum of the reciprocals of the positive divisors of a number

Published on 29 Mar 2019 - 5:08

score 70 · Answer 14 · 2019-03-31 07:30:56

70

Views

Generalise of $\sigma_k(P_a^j)+\sigma_k(P^{j+1}_a)?$

Published on 31 Mar 2019 - 7:30

score 70 · Answer 15 · 2026-02-23 01:23:01

70

Views

If $q$ is a Fermat prime, is $\sigma(q^k)/2$ a square if $k \equiv 1 \pmod 4$?

Published on 23 Feb 2026 - 1:23

List Question

If $\sigma(n) = 2n - d$ and $d \mid n$, is it true that $d = \gcd(n,\sigma(n))$?

Improving the bound for $\sigma(q^k)/q^k$ where $q^k n^2$ is an odd perfect number given in Eulerian form

Either $np$ is even, or $n^2 − p^2$ is a multiple of $8$.

Can these bounds in terms of the abundancy index and deficiency functions be improved for deficient-perfect numbers?

A consequence of assuming the Descartes-Frenicle-Sorli Conjecture on odd perfect numbers

If $\sigma(n)/n = 5/3$, then $5 \nmid n$. Does it also follow that $3 \nmid \sigma(n)$?

On the golden ratio and odd perfect numbers

What is $\sigma(q^k)$ in terms of $k$ if $q \equiv 5 \pmod 8$?

On GCDs and odd perfect numbers

Breaking the barriers at $q=5$ and $q=13$ for $q^k n^2$ an odd perfect number with special prime $q$

Is this $\zeta(p)=\sum_{k\geq1 ,p\in \mathbb{P}}\frac{1}{{\sigma}_k(p)-1}$ true with sigma is power of sum divisor function?

Sum of all positive divisors are prime

Finding the sum of the reciprocals of the positive divisors of a number

Generalise of $\sigma_k(P_a^j)+\sigma_k(P^{j+1}_a)?$

If $q$ is a Fermat prime, is $\sigma(q^k)/2$ a square if $k \equiv 1 \pmod 4$?

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