Question

On the abundancy index of divisors of odd perfect numbers and a possible upper bound for the special/Euler prime

score 143 · Answer 1 · 2026-04-24 18:55:40

143

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On the abundancy index of divisors of odd perfect numbers and a possible upper bound for the special/Euler prime

Published on 24 Apr 2026 - 18:55

score 72 · Answer 2 · 2026-03-26 07:59:21

72

Views

If $a$ is deficient-perfect, can $ab$ be deficient-perfect if $b > 1$, and $ab$ is odd?

Published on 26 Mar 2026 - 7:59

score 118 · Answer 3 · 2026-04-17 05:17:33

118

Views

On a superior limit involving the multiplication formula for the Gamma function and the divisors $d\mid n$ of a positive integer

Published on 17 Apr 2026 - 5:17

score 727 · Answer 4 · 2026-04-14 22:14:58

727

Views

a formula involving order of Dirichlet characters, $\mu(n)$ and $\varphi(n)$

Published on 14 Apr 2026 - 22:14

score 293 · Answer 5 · 2026-04-13 01:35:35

293

Views

Convolution product of arithmetic functions

Published on 13 Apr 2026 - 1:35

score 244 · Answer 6 · 2026-04-15 03:40:03

244

Views

Does make sense a generalization of Lagarias equivalence with $H_n^s=1+1/2^s+\ldots+1/n^s$ and $\sigma^s(n)=\sum_{k\mid n}k^s$, for $\Re s>1$?

Published on 15 Apr 2026 - 3:40

score 90 · Answer 7 · 2026-04-16 13:23:52

90

Views

What is a sharp upper bound for $\prod_{i=1}^{r}{\left({p_i}^{\alpha_i} - \sigma({p_i}^{\alpha_i - 1})\right)}?$

Published on 16 Apr 2026 - 13:23

score 44 · Answer 8 · 2026-04-16 15:50:20

44

Views

If $D(m)$ is the deficiency of the deficient number $m$, then what is $\lim_{m \rightarrow \infty}{\frac{D(m)}{m}}$?

Published on 16 Apr 2026 - 15:50

score 54 · Answer 9 · 2026-04-12 07:13:28

54

Views

For what numbers $x$ is $D(x) = 2x - \sigma_1(x)$ equal to $\varphi(x)$?

Published on 12 Apr 2026 - 7:13

score 81 · Answer 10 · 2026-04-15 11:37:31

81

Views

Is the following statement true if $N = q^k n^2$ is an odd perfect number given in Eulerian form?

Published on 15 Apr 2026 - 11:37

score 69 · Answer 11 · 2026-05-11 01:29:49

69

Views

On interesting definitions involving the sum of remainders function and sequences of integers with special abundancy

Published on 11 May 2026 - 1:29

score 265 · Answer 12 · 2026-04-15 02:05:07

265

Views

What is the smallest solution of the congruence $a^{x} \equiv 1 (\textrm{mod}\ n)$?

Published on 15 Apr 2026 - 2:05

score 107 · Answer 13 · 2026-05-11 02:50:18

107

Views

On a sequence with $n^{\frac{1}{\operatorname{rad}(n)}}$ unbounded, where $\operatorname{rad}(n)$ is the product of primes dividing $n$

Published on 11 May 2026 - 2:50

score 203 · Answer 14 · 2026-04-13 14:26:43

203

Views

Does $k=9018009$ have a friend?

Published on 13 Apr 2026 - 14:26

score 175 · Answer 15 · 2026-04-16 01:13:39

175

Views

If $q^k n^2$ is an odd perfect number with Euler prime $q$, can $q=17$ hold?

Published on 16 Apr 2026 - 1:13

List Question

On the abundancy index of divisors of odd perfect numbers and a possible upper bound for the special/Euler prime

If $a$ is deficient-perfect, can $ab$ be deficient-perfect if $b > 1$, and $ab$ is odd?

On a superior limit involving the multiplication formula for the Gamma function and the divisors $d\mid n$ of a positive integer

a formula involving order of Dirichlet characters, $\mu(n)$ and $\varphi(n)$

Convolution product of arithmetic functions

Does make sense a generalization of Lagarias equivalence with $H_n^s=1+1/2^s+\ldots+1/n^s$ and $\sigma^s(n)=\sum_{k\mid n}k^s$, for $\Re s>1$?

What is a sharp upper bound for $\prod_{i=1}^{r}{\left({p_i}^{\alpha_i} - \sigma({p_i}^{\alpha_i - 1})\right)}?$

If $D(m)$ is the deficiency of the deficient number $m$, then what is $\lim_{m \rightarrow \infty}{\frac{D(m)}{m}}$?

For what numbers $x$ is $D(x) = 2x - \sigma_1(x)$ equal to $\varphi(x)$?

Is the following statement true if $N = q^k n^2$ is an odd perfect number given in Eulerian form?

On interesting definitions involving the sum of remainders function and sequences of integers with special abundancy

What is the smallest solution of the congruence $a^{x} \equiv 1 (\textrm{mod}\ n)$?

On a sequence with $n^{\frac{1}{\operatorname{rad}(n)}}$ unbounded, where $\operatorname{rad}(n)$ is the product of primes dividing $n$

Does $k=9018009$ have a friend?

If $q^k n^2$ is an odd perfect number with Euler prime $q$, can $q=17$ hold?

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