List questions from arithmetic-functions

Published on 12 Apr 2026 - 19:06

410

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How to show that $\prod_{d/n} d = n^{\frac{\tau(n)}{2}}$

Published on 16 Apr 2026 - 17:45

127

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Is there a way to show that $d(n)$, which counts the number of divisors of $n$ is non-increasing?

Published on 17 Apr 2026 - 4:12

130

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Are there particular techniques to find the general formula for an arithmetic function, neither multiplicative nor additive?

Published on 11 Apr 2026 - 16:10

4.6k

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Proving $\phi(m)|\phi(n)$ whenever $m|n$

Published on 15 Apr 2026 - 3:32

135

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Show that $\sum_{i=1}^{n}(i-1,n)[(i,n)=1] = \phi(n) \sigma_0(n)$

Published on 14 Apr 2026 - 21:27

167

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About the 'sigma' function.

Published on 09 Apr 2026 - 15:55

90

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gcd of product of exponents of prime factors and product of prime factors

Published on 11 Apr 2026 - 20:46

68

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What is the inverse of $f(x)=x^{x^x}$?

Published on 15 Apr 2026 - 3:45

208

Views

Prime Factorization and Number Theory

Published on 14 Apr 2026 - 13:26

158

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How many numbers are products of $p^p$?

Published on 10 Apr 2026 - 21:12

425

Views

Where did the sum-of-divisors function come from?

Published on 12 Apr 2026 - 3:20

110

Views

Number of triples $(a, b, c)$ with $1 \leq a,b,c \leq n$ which are coprime ($gcd(a,b,c)=1$)

Published on 16 Apr 2026 - 8:14

391

Views

Inequality $\varphi(N)>\pi(N)$?

Published on 11 Apr 2026 - 22:24

2.5k

Views

Prove there are k consecutive non-squarefree integers

Published on 12 Apr 2026 - 20:09

List Question

sum over primes involving divisor function (variation of the Titchmarsh divisor problem)

How to show that $\prod_{d/n} d = n^{\frac{\tau(n)}{2}}$

Is there a way to show that $d(n)$, which counts the number of divisors of $n$ is non-increasing?

Are there particular techniques to find the general formula for an arithmetic function, neither multiplicative nor additive?

Proving $\phi(m)|\phi(n)$ whenever $m|n$

Show that $\sum_{i=1}^{n}(i-1,n)[(i,n)=1] = \phi(n) \sigma_0(n)$

About the 'sigma' function.

gcd of product of exponents of prime factors and product of prime factors

What is the inverse of $f(x)=x^{x^x}$?

Prime Factorization and Number Theory

How many numbers are products of $p^p$?

Where did the sum-of-divisors function come from?

Number of triples $(a, b, c)$ with $1 \leq a,b,c \leq n$ which are coprime ($gcd(a,b,c)=1$)

Inequality $\varphi(N)>\pi(N)$?

Prove there are k consecutive non-squarefree integers

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