Question

$\phi(n)^{\sigma(n)^{\tau(n)}}=n^2$ find all natural numbers $n$ such that the equality is true

score 356 · Answer 1 · 2026-04-22 23:30:31

356

Views

$\phi(n)^{\sigma(n)^{\tau(n)}}=n^2$ find all natural numbers $n$ such that the equality is true

Published on 22 Apr 2026 - 23:30

score 351 · Answer 2 · 2026-05-10 14:29:23

351

Views

Is it possible to simplify this expression even further?

Published on 10 May 2026 - 14:29

score 62 · Answer 3 · 2026-04-17 11:42:39

62

Views

Around the equation $4\,\varphi \left(2^{n-1} \sigma(n)\right) ^2=2^{\sigma(n)}\cdot\varphi(n)^2$

Published on 17 Apr 2026 - 11:42

score 49 · Answer 4 · 2026-04-14 19:46:40

49

Views

Prove this factorial fractional equivalence

Published on 14 Apr 2026 - 19:46

score 87 · Answer 5 · 2026-04-12 18:53:41

87

Views

Is 31 the only number that can be represented by two distinct sums of consecutive powers of primes?

Published on 12 Apr 2026 - 18:53

score 92 · Answer 6 · 2026-04-16 07:44:24

92

Views

Is ${n^2}/D(n^2) \in \mathbb{N}$, if $q^k n^2$ is an odd perfect number?

Published on 16 Apr 2026 - 7:44

score 759 · Answer 7 · 2026-04-16 00:30:37

759

Views

Are there any natural numbers $n$ that satisfy the condition $7921\sigma(n) = 15840n$?

Published on 16 Apr 2026 - 0:30

score 85 · Answer 8 · 2026-04-14 06:14:17

85

Views

Do positive integers $a,b,c,d$ exist with the given properties?

Published on 14 Apr 2026 - 6:14

score 81 · Answer 9 · 2026-04-13 00:08:25

81

Views

Specific evidence for or against the Descartes-Frenicle-Sorli conjecture on odd perfect numbers

Published on 13 Apr 2026 - 0:08

score 143 · Answer 10 · 2026-04-15 12:25:36

143

Views

Is $198585576189$ a member of OEIS sequence A228059?

Published on 15 Apr 2026 - 12:25

score 56 · Answer 11 · 2026-04-15 15:45:44

56

Views

On the quantity ${n^2}/D(n^2)$ where $n^2$ is the non-Euler part of members of the OEIS sequence A228059

Published on 15 Apr 2026 - 15:45

score 841 · Answer 12 · 2026-04-16 09:44:59

841

Views

Solutions of the equation $(m! + 2)\sigma(n) = 2n \cdot m!$ where $5 \leq m$

Published on 16 Apr 2026 - 9:44

score 389 · Answer 13 · 2026-04-12 19:26:22

389

Views

Can a composite number $n$ be the arithmetic mean of $\sigma(n)$ and $\varphi(n)$?

Published on 12 Apr 2026 - 19:26

score 120 · Answer 14 · 2026-04-10 11:35:16

120

Views

What are the properties of abundancy numbers?

Published on 10 Apr 2026 - 11:35

score 263 · Answer 15 · 2026-04-14 18:47:09

263

Views

Are all numbers of the type $\frac{n!}{2}+1$ deficient?

Published on 14 Apr 2026 - 18:47

List Question

$\phi(n)^{\sigma(n)^{\tau(n)}}=n^2$ find all natural numbers $n$ such that the equality is true

Is it possible to simplify this expression even further?

Around the equation $4\,\varphi \left(2^{n-1} \sigma(n)\right) ^2=2^{\sigma(n)}\cdot\varphi(n)^2$

Prove this factorial fractional equivalence

Is 31 the only number that can be represented by two distinct sums of consecutive powers of primes?

Is ${n^2}/D(n^2) \in \mathbb{N}$, if $q^k n^2$ is an odd perfect number?

Are there any natural numbers $n$ that satisfy the condition $7921\sigma(n) = 15840n$?

Do positive integers $a,b,c,d$ exist with the given properties?

Specific evidence for or against the Descartes-Frenicle-Sorli conjecture on odd perfect numbers

Is $198585576189$ a member of OEIS sequence A228059?

On the quantity ${n^2}/D(n^2)$ where $n^2$ is the non-Euler part of members of the OEIS sequence A228059

Solutions of the equation $(m! + 2)\sigma(n) = 2n \cdot m!$ where $5 \leq m$

Can a composite number $n$ be the arithmetic mean of $\sigma(n)$ and $\varphi(n)$?

What are the properties of abundancy numbers?

Are all numbers of the type $\frac{n!}{2}+1$ deficient?

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