Question

Is there an analytical solution to the inequality $\frac{1 + k({p}^{(k+1)/2)})}{p^k} < \frac{p}{p - 1}$ if one were to bound $k$ in terms of $p$?

score 102 · Answer 1 · 2023-02-15 07:47:52

102

Views

Is there an analytical solution to the inequality $\frac{1 + k({p}^{(k+1)/2)})}{p^k} < \frac{p}{p - 1}$ if one were to bound $k$ in terms of $p$?

Published on 15 Feb 2023 - 7:47

score 53 · Answer 2 · 2026-03-25 14:46:55

53

Views

Is the set of divisor indicator functions at $x^2 - 1$: $B' = \{(d \mid x^2 - 1) : d \in \Bbb{N}\}$ a $\Bbb{Z}$-linearly independent set?

Published on 25 Mar 2026 - 14:46

score 70 · Answer 3 · 2023-02-17 06:29:52

70

Views

Weird arithmetics with prime numbers...

Published on 17 Feb 2023 - 6:29

score 121 · Answer 4 · 2026-03-26 13:45:56

121

Views

Is this disproof for the Descartes-Frenicle-Sorli Conjecture that $k=1$, if $p^k m^2$ is an odd perfect number, valid?

Published on 26 Mar 2026 - 13:45

score 22 · Answer 5 · 2023-03-18 12:20:09

22

Views

Arithmetic Progression/Sequence | Does it include terms prior to the initial term?

Published on 18 Mar 2023 - 12:20

score 41 · Answer 6 · 2026-03-26 13:45:56

41

Views

Is this proof for the divisibility constraint $\sigma(q^k)/2 \mid n$ correct, where $q^k n^2$ is an odd perfect number with special prime $q$?

Published on 26 Mar 2026 - 13:45

score 47 · Answer 7 · 2023-03-25 10:10:15

47

Views

Is there an algorithm to solve number manipulation problems?

Published on 25 Mar 2023 - 10:10

score 56 · Answer 8 · 2023-04-20 07:42:25

56

Views

Pointwise Extension of Multiplicativity

Published on 20 Apr 2023 - 7:42

score 705 · Answer 9 · 2023-04-25 12:47:03

705

Views

Almost exact formula for sum of Euler Phi function $\sum_{k=1}^n \varphi(k)$

Published on 25 Apr 2023 - 12:47

score 181 · Answer 10 · 2026-03-26 13:46:37

181

Views

Does an odd perfect number have a divisor (other than $1$) which must necessarily be almost perfect?

Published on 26 Mar 2026 - 13:46

score 117 · Answer 11 · 2023-05-19 10:20:46

117

Views

A problem on von Mangoldt function.

Published on 19 May 2023 - 10:20

score 129 · Answer 12 · 2026-03-25 17:52:50

129

Views

If an arithmetic function is multiplicative, non-zero at a prime, and "prime-linear", is it the identity?

Published on 25 Mar 2026 - 17:52

score 71 · Answer 13 · 2026-03-25 22:03:26

71

Views

How to get the Euler product for $\sum_{n = 1}^{\infty} \mu(n)/\phi(n^k)$.

Published on 25 Mar 2026 - 22:03

score 90 · Answer 14 · 2023-07-07 12:47:29

90

Views

Verify if exists $n$ such that $\phi(n)$ equals $\frac{n}{d}$, for a constant $d$

Published on 07 Jul 2023 - 12:47

score 36 · Answer 15 · 2023-07-21 15:28:40

36

Views

Connection between multiplication table $n * k$ and partial sums of the partial sums of the Dirichlet inverse of the Euler totient function.

Published on 21 Jul 2023 - 15:28

List Question

Is there an analytical solution to the inequality $\frac{1 + k({p}^{(k+1)/2)})}{p^k} < \frac{p}{p - 1}$ if one were to bound $k$ in terms of $p$?

Is the set of divisor indicator functions at $x^2 - 1$: $B' = \{(d \mid x^2 - 1) : d \in \Bbb{N}\}$ a $\Bbb{Z}$-linearly independent set?

Weird arithmetics with prime numbers...

Is this disproof for the Descartes-Frenicle-Sorli Conjecture that $k=1$, if $p^k m^2$ is an odd perfect number, valid?

Arithmetic Progression/Sequence | Does it include terms prior to the initial term?

Is this proof for the divisibility constraint $\sigma(q^k)/2 \mid n$ correct, where $q^k n^2$ is an odd perfect number with special prime $q$?

Is there an algorithm to solve number manipulation problems?

Pointwise Extension of Multiplicativity

Almost exact formula for sum of Euler Phi function $\sum_{k=1}^n \varphi(k)$

Does an odd perfect number have a divisor (other than $1$) which must necessarily be almost perfect?

A problem on von Mangoldt function.

If an arithmetic function is multiplicative, non-zero at a prime, and "prime-linear", is it the identity?

How to get the Euler product for $\sum_{n = 1}^{\infty} \mu(n)/\phi(n^k)$.

Verify if exists $n$ such that $\phi(n)$ equals $\frac{n}{d}$, for a constant $d$

Connection between multiplication table $n * k$ and partial sums of the partial sums of the Dirichlet inverse of the Euler totient function.

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