Question

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

score 352 · Answer 1 · 2026-03-21 19:30:22

352

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

Published on 21 Mar 2026 - 19:30

score 347 · Answer 2 · 2026-03-17 13:15:58

347

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Is it possible to simplify this expression even further?

Published on 17 Mar 2026 - 13:15

score 59 · Answer 3 · 2018-06-26 17:23:25

59

Views

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

Published on 26 Jun 2018 - 17:23

score 45 · Answer 4 · 2018-07-01 15:41:08

45

Views

Prove this factorial fractional equivalence

Published on 01 Jul 2018 - 15:41

score 84 · Answer 5 · 2018-07-15 06:51:45

84

Views

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

Published on 15 Jul 2018 - 6:51

score 89 · Answer 6 · 2018-07-19 22:33:40

89

Views

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

Published on 19 Jul 2018 - 22:33

score 757 · Answer 7 · 2018-07-20 07:57:03

757

Views

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

Published on 20 Jul 2018 - 7:57

score 82 · Answer 8 · 2018-07-22 12:57:43

82

Views

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

Published on 22 Jul 2018 - 12:57

score 78 · Answer 9 · 2018-08-02 12:46:06

78

Views

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

Published on 02 Aug 2018 - 12:46

score 140 · Answer 10 · 2018-08-03 06:08:04

140

Views

Is $198585576189$ a member of OEIS sequence A228059?

Published on 03 Aug 2018 - 6:08

score 54 · Answer 11 · 2018-08-03 09:02:35

54

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 03 Aug 2018 - 9:02

score 838 · Answer 12 · 2018-08-05 13:51:38

838

Views

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

Published on 05 Aug 2018 - 13:51

score 386 · Answer 13 · 2018-08-07 23:04:32

386

Views

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

Published on 07 Aug 2018 - 23:04

score 116 · Answer 14 · 2018-08-13 13:03:34

116

Views

What are the properties of abundancy numbers?

Published on 13 Aug 2018 - 13:03

score 260 · Answer 15 · 2018-08-14 11:54:17

260

Views

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

Published on 14 Aug 2018 - 11:54

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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