List questions from arithmetic-functions

Published on 27 Mar 2026 - 23:48

75

Views

If $\sigma(n) \equiv 2 \pmod 4$ and $n$ is odd, does this imply that $n = p^k m^2$?

Published on 25 Apr 2017 - 14:43

508

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Why is it impossible for phi(n) = 14?

Published on 07 May 2017 - 20:47

68

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About a more efficient way of evaluating $L(n):=\sum_{k=1}^n\lambda(k)$, where $\lambda(n)$ is the Liouville function, than this definition of $L(n)$

Published on 09 May 2017 - 16:06

509

Views

Find all positive integers $n$ such that $\phi(\phi(n))=2$

Published on 14 May 2017 - 6:57

67

Views

Residue class of prime powers

Published on 16 May 2017 - 20:57

69

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How to formalize that proof

Published on 19 May 2017 - 18:18

63

Views

A strange multiplicative function

Published on 26 Mar 2026 - 2:33

1.3k

Views

Euler's totient function of a product for arbitrary n and m

Published on 30 May 2017 - 20:27

143

Views

Some regularity in the prime decomposition

Published on 12 Jun 2017 - 14:55

189

Views

An estimate of the second moment of the Ramanujan $\tau$- function

Published on 24 Jun 2017 - 3:19

91

Views

How often does $D(n^2) = m^2$ happen, where $D(x)$ is the deficiency of $x$?

Published on 29 Jun 2017 - 15:33

160

Views

Do there exist deficient-perfect square numbers whose deficiency is also a square (and not one)?

Published on 30 Jun 2017 - 2:57

133

Views

First step with the equation $\sigma(n)=\phi(n)+\operatorname{rad}(n)$: a first statement

Published on 30 Jun 2017 - 14:40

34

Views

On inequalities concerning a certain function $F$

Published on 04 Jul 2017 - 10:07

List Question

Arithmetic function

If $\sigma(n) \equiv 2 \pmod 4$ and $n$ is odd, does this imply that $n = p^k m^2$?

Why is it impossible for phi(n) = 14?

About a more efficient way of evaluating $L(n):=\sum_{k=1}^n\lambda(k)$, where $\lambda(n)$ is the Liouville function, than this definition of $L(n)$

Find all positive integers $n$ such that $\phi(\phi(n))=2$

Residue class of prime powers

How to formalize that proof

A strange multiplicative function

Euler's totient function of a product for arbitrary n and m

Some regularity in the prime decomposition

An estimate of the second moment of the Ramanujan $\tau$- function

How often does $D(n^2) = m^2$ happen, where $D(x)$ is the deficiency of $x$?

Do there exist deficient-perfect square numbers whose deficiency is also a square (and not one)?

First step with the equation $\sigma(n)=\phi(n)+\operatorname{rad}(n)$: a first statement

On inequalities concerning a certain function $F$

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