Question

On miscellaneous questions about perfect numbers I

score 49 · Answer 1 · 2026-03-17 06:15:35

49

Views

On miscellaneous questions about perfect numbers I

Published on 17 Mar 2026 - 6:15

score 69 · Answer 2 · 2026-03-17 06:15:23

69

Views

On miscellaneous questions about perfect numbers II

Published on 17 Mar 2026 - 6:15

score 102 · Answer 3 · 2026-03-20 02:59:17

102

Views

On miscellaneous questions about perfect numbers III

Published on 20 Mar 2026 - 2:59

score 221 · Answer 4 · 2018-04-03 22:00:02

221

Views

On the equation involving the sum of divisors function $\sigma(105n+\sigma(n))=108\sigma(n)$

Published on 03 Apr 2018 - 22:00

score 55 · Answer 5 · 2026-03-17 21:17:32

55

Views

Are all denominators of $\zeta(2n)$ abundant, for $n\geq2$?

Published on 17 Mar 2026 - 21:17

score 42 · Answer 6 · 2026-03-17 07:56:23

42

Views

Does there exist a natural number $N = xy$ satisfying $D(x)D(y) = 2s(x)s(y)$ with $\gcd(x,y)=1$?

Published on 17 Mar 2026 - 7:56

score 45 · Answer 7 · 2018-04-12 11:26:55

45

Views

Does there exist an odd natural number $N = xy$ satisfying $D(x)D(y) = 2s(x)s(y)$?

Published on 12 Apr 2018 - 11:26

score 393 · Answer 8 · 2026-03-24 22:08:42

393

Views

If $n = km$ is a Descartes number with quasi-Euler prime $m$, then $m < k$.

Published on 24 Mar 2026 - 22:08

score 148 · Answer 9 · 2018-04-20 10:03:26

148

Views

Equations involving arithmetic functions, totatives and even perfect numbers

Published on 20 Apr 2018 - 10:03

score 58 · Answer 10 · 2026-03-10 12:53:20

58

Views

Deduce the number of divisors, $d(n)$ is multiplicative and obtain a formula of $d(n)$ in terms of prime decomposition

Published on 10 Mar 2026 - 12:53

score 114 · Answer 11 · 2018-04-22 19:52:13

114

Views

For the number of divisors function, $d(n)$, deduce all positive integers when $d(n)$ is odd

Published on 22 Apr 2018 - 19:52

score 106 · Answer 12 · 2018-04-25 10:57:23

106

Views

A problem similar than that of the amicable pairs using the function $\operatorname{rad}(k)$: a first statement or conjecture

Published on 25 Apr 2018 - 10:57

score 101 · Answer 13 · 2026-03-17 11:02:52

101

Views

Where is the mistake in the argument? (And two conjectures)

Published on 17 Mar 2026 - 11:02

score 863 · Answer 14 · 2026-03-23 02:51:26

863

Views

A conjecture concerning the number of divisors and the sum of divisors.

Published on 23 Mar 2026 - 2:51

score 100 · Answer 15 · 2018-05-03 14:48:17

100

Views

Can the following argument be pushed to a full proof that $(p + 2)/p$ is an outlaw if $p$ is an odd prime?

Published on 03 May 2018 - 14:48

List Question

On miscellaneous questions about perfect numbers I

On miscellaneous questions about perfect numbers II

On miscellaneous questions about perfect numbers III

On the equation involving the sum of divisors function $\sigma(105n+\sigma(n))=108\sigma(n)$

Are all denominators of $\zeta(2n)$ abundant, for $n\geq2$?

Does there exist a natural number $N = xy$ satisfying $D(x)D(y) = 2s(x)s(y)$ with $\gcd(x,y)=1$?

Does there exist an odd natural number $N = xy$ satisfying $D(x)D(y) = 2s(x)s(y)$?

If $n = km$ is a Descartes number with quasi-Euler prime $m$, then $m < k$.

Equations involving arithmetic functions, totatives and even perfect numbers

Deduce the number of divisors, $d(n)$ is multiplicative and obtain a formula of $d(n)$ in terms of prime decomposition

For the number of divisors function, $d(n)$, deduce all positive integers when $d(n)$ is odd

A problem similar than that of the amicable pairs using the function $\operatorname{rad}(k)$: a first statement or conjecture

Where is the mistake in the argument? (And two conjectures)

A conjecture concerning the number of divisors and the sum of divisors.

Can the following argument be pushed to a full proof that $(p + 2)/p$ is an outlaw if $p$ is an odd prime?

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