List questions from multiplicative-function

Published on 24 May 2020 - 15:40

34

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Show $\sum_{c|n} \mu(c)f(c) = \{1-f(p_1)\}\{1-f(p_2)\} \dots \{1-f(p_r)\}$

Published on 12 Jun 2020 - 13:14

291

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Sum of divisors function inequality

Published on 21 Jun 2020 - 0:43

185

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find all $n$ such that $\varphi(\sigma(2^n)) = 2^n$

Published on 24 Jun 2020 - 21:48

65

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Prove of $\prod_{d|n} (\mu(d)(\mu(d) + 3) + 4) = 4^{d(n)}$

Published on 04 Jul 2020 - 20:41

1.1k

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Is $\sum_{d | n} f(d)$ completely multiplicative if $f$ is completely multiplicative?

Published on 29 Jul 2016 - 23:15

75

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Uniqueness of $f( x y - 1) = f(x-1)f(y-1),f(1) = A,f(1+n)>f(n)$?

Published on 08 Aug 2016 - 9:56

139

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Optimal multiplying method

Published on 09 Aug 2016 - 0:39

70

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Infinite Product for Multiplicative Functions

Published on 17 Sep 2016 - 2:06

8.9k

Views

The sigma function (sum of divisors) multiplicative proof

Published on 30 Sep 2016 - 19:20

63

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What is the largest (if any) multiplicative modulo group with all prime elements?

Published on 02 Oct 2016 - 14:33

465

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Does the Mobius Inversion Theorem hold when sum function is over multiples instead of divisors

Published on 12 Oct 2016 - 15:06

1.7k

Views

Show that $f(n) = \gcd(a,n)$ is a multiplicative function

Published on 20 Oct 2016 - 21:14

1.5k

Views

Formula for square of the number of divisors $\sum_{r\mid n} d(r^2) = d^2(n)$

Published on 23 Mar 2026 - 15:43

45

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Is there any way to simplify this function?

Published on 03 Nov 2016 - 16:31

List Question

Why does the divisor-counting function appear in bounds for Kloosterman sums?

Show $\sum_{c|n} \mu(c)f(c) = \{1-f(p_1)\}\{1-f(p_2)\} \dots \{1-f(p_r)\}$

Sum of divisors function inequality

find all $n$ such that $\varphi(\sigma(2^n)) = 2^n$

Prove of $\prod_{d|n} (\mu(d)(\mu(d) + 3) + 4) = 4^{d(n)}$

Is $\sum_{d | n} f(d)$ completely multiplicative if $f$ is completely multiplicative?

Uniqueness of $f( x y - 1) = f(x-1)f(y-1),f(1) = A,f(1+n)>f(n)$?

Optimal multiplying method

Infinite Product for Multiplicative Functions

The sigma function (sum of divisors) multiplicative proof

What is the largest (if any) multiplicative modulo group with all prime elements?

Does the Mobius Inversion Theorem hold when sum function is over multiples instead of divisors

Show that $f(n) = \gcd(a,n)$ is a multiplicative function

Formula for square of the number of divisors $\sum_{r\mid n} d(r^2) = d^2(n)$

Is there any way to simplify this function?

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