Question

On odd perfect numbers $q^k n^2$ and the deficient-perfect divisor $q^{\frac{k-1}{2}} n^2$ - Part II

score 128 · Answer 1 · 2026-03-27 10:12:53

128

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On odd perfect numbers $q^k n^2$ and the deficient-perfect divisor $q^{\frac{k-1}{2}} n^2$ - Part II

Published on 27 Mar 2026 - 10:12

score 119 · Answer 2 · 2026-03-28 12:14:06

119

Views

Is this expression bounded when $p \equiv 1 \pmod 4$ is prime and $t \equiv 1 \pmod 4$?

Published on 28 Mar 2026 - 12:14

score 142 · Answer 3 · 2026-03-27 14:57:47

142

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Is this proof regarding odd perfect numbers valid?

Published on 27 Mar 2026 - 14:57

score 70 · Answer 4 · 2020-10-24 08:22:54

70

Views

On the existence of odd, squarefree semiperfect numbers

Published on 24 Oct 2020 - 8:22

score 127 · Answer 5 · 2026-03-26 07:39:13

127

Views

Proving a relation between sum of reciprocal of divisors and $\sigma(n)$

Published on 26 Mar 2026 - 7:39

score 139 · Answer 6 · 2020-10-30 12:57:35

139

Views

A Collatz like function or Eulers totient function vs. the sum of divisors?

Published on 30 Oct 2020 - 12:57

score 154 · Answer 7 · 2026-03-27 10:12:59

154

Views

On the quantity $I(q^k) + I(n^2)$ where $q^k n^2$ is an odd perfect number with special prime $q$

Published on 27 Mar 2026 - 10:12

score 243 · Answer 8 · 2026-03-28 12:14:42

243

Views

Is it possible to improve on the bound $D(q^k) < \varphi(q^k)$ if $k > 1$?

Published on 28 Mar 2026 - 12:14

score 173 · Answer 9 · 2020-11-09 00:34:03

173

Views

Sum of divisors in terms of their prime factors

Published on 09 Nov 2020 - 0:34

score 92 · Answer 10 · 2020-11-09 16:15:59

92

Views

How to approach the negative root of the series $\sum\limits_{k=1}^{\infty} \sigma_1(k) x^k$

Published on 09 Nov 2020 - 16:15

score 259 · Answer 11 · 2026-03-27 10:10:52

259

Views

On the nearest-square function - Part 2 and the quantity $m^2 - p^k$ where $p^k m^2$ is an odd perfect number

Published on 27 Mar 2026 - 10:10

score 41 · Answer 12 · 2020-11-11 12:07:29

41

Views

On the number of prime divisors of a product of 4 consecutive integers

Published on 11 Nov 2020 - 12:07

score 69 · Answer 13 · 2020-11-14 13:25:47

69

Views

Estimate of $\prod_{d\mid n}(d+1)$.

Published on 14 Nov 2020 - 13:25

score 46 · Answer 14 · 2020-11-15 10:25:01

46

Views

Does this inequality hold for all odd $n$: $\sigma_{n-1}\sigma_{n+3} > \sigma_{n}\sigma_{n+2}$?

Published on 15 Nov 2020 - 10:25

score 239 · Answer 15 · 2026-03-27 10:12:08

239

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If $p^k m^2$ is an odd perfect number, then what is the optimal constant $C$ such that $\frac{\sigma(m^2)}{p^k} < \frac{m^2 - p^k}{C}$?

Published on 27 Mar 2026 - 10:12

List Question

On odd perfect numbers $q^k n^2$ and the deficient-perfect divisor $q^{\frac{k-1}{2}} n^2$ - Part II

Is this expression bounded when $p \equiv 1 \pmod 4$ is prime and $t \equiv 1 \pmod 4$?

Is this proof regarding odd perfect numbers valid?

On the existence of odd, squarefree semiperfect numbers

Proving a relation between sum of reciprocal of divisors and $\sigma(n)$

A Collatz like function or Eulers totient function vs. the sum of divisors?

On the quantity $I(q^k) + I(n^2)$ where $q^k n^2$ is an odd perfect number with special prime $q$

Is it possible to improve on the bound $D(q^k) < \varphi(q^k)$ if $k > 1$?

Sum of divisors in terms of their prime factors

How to approach the negative root of the series $\sum\limits_{k=1}^{\infty} \sigma_1(k) x^k$

On the nearest-square function - Part 2 and the quantity $m^2 - p^k$ where $p^k m^2$ is an odd perfect number

On the number of prime divisors of a product of 4 consecutive integers

Estimate of $\prod_{d\mid n}(d+1)$.

Does this inequality hold for all odd $n$: $\sigma_{n-1}\sigma_{n+3} > \sigma_{n}\sigma_{n+2}$?

If $p^k m^2$ is an odd perfect number, then what is the optimal constant $C$ such that $\frac{\sigma(m^2)}{p^k} < \frac{m^2 - p^k}{C}$?

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