List questions from multiplicative-function

Published on 24 Mar 2026 - 20:57

671

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Minimum possible value of $f(2007)$ where $f(m f(n)) = n f(m)$, $m,n\in \Bbb N$

Published on 25 Mar 2026 - 2:35

81

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Are there (restricted) instances when the deficiency and sum-of-proper-divisors functions are multiplicative?

Published on 24 Mar 2026 - 3:03

31

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Karatsuba Multiplication Rule in dividing a Number in two parts

Published on 24 Mar 2026 - 1:11

1k

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Let $(a_n)$ be a strictly increasing sequence of positive integers such that: $a_2 = 2$, $a_{mn} = a_m a_n$ for $m, n$ relatively prime.

Published on 23 Mar 2026 - 20:17

1k

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Prove that if $d \mid n \in \mathbb{N}$, then $\varphi(d) \mid \varphi(n)$.

Published on 25 Mar 2026 - 4:19

2.9k

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Is there a recursive formula for Euler's Totient function

Published on 25 Mar 2026 - 0:21

3.8k

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Prove that if d = gcd(m,n) then $\phi(mn)=\phi(m)*\phi(n)/d$

Published on 24 Mar 2026 - 19:51

61

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Summatory Function $F(n) = 1 $ for all $n$ odd, and $F(n) = 2$ for all n even

Published on 24 Mar 2026 - 20:43

444

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How prove this $\sum_{t|n}(d(t))^3=\left(\sum_{t|n}d(t)\right)^2$

Published on 24 Mar 2026 - 19:41

1.2k

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Multiplicative inverses and co-primes

Published on 24 Mar 2026 - 18:42

1.6k

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Why f(1)=1 for every multiplicative function f?

Published on 23 Mar 2026 - 22:18

456

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Closed formula for a multiple Dirichlet convolution of the 1-function with the identity

Published on 13 May 2014 - 23:22

1.8k

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How to find all elements in Z/80 that have multiplicative inverses.

Published on 24 Mar 2026 - 16:43

83

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When is $f(n)=\sum\limits_{d\mid n}\sigma(d)$ prime?

Published on 23 Mar 2026 - 16:33

List Question

Closed-form for $F(n) = \sum_{d|n} \omega_x(d) $

Minimum possible value of $f(2007)$ where $f(m f(n)) = n f(m)$, $m,n\in \Bbb N$

Are there (restricted) instances when the deficiency and sum-of-proper-divisors functions are multiplicative?

Karatsuba Multiplication Rule in dividing a Number in two parts

Let $(a_n)$ be a strictly increasing sequence of positive integers such that: $a_2 = 2$, $a_{mn} = a_m a_n$ for $m, n$ relatively prime.

Prove that if $d \mid n \in \mathbb{N}$, then $\varphi(d) \mid \varphi(n)$.

Is there a recursive formula for Euler's Totient function

Prove that if d = gcd(m,n) then $\phi(mn)=\phi(m)*\phi(n)/d$

Summatory Function $F(n) = 1 $ for all $n$ odd, and $F(n) = 2$ for all n even

How prove this $\sum_{t|n}(d(t))^3=\left(\sum_{t|n}d(t)\right)^2$

Multiplicative inverses and co-primes

Why f(1)=1 for every multiplicative function f?

Closed formula for a multiple Dirichlet convolution of the 1-function with the identity

How to find all elements in Z/80 that have multiplicative inverses.

When is $f(n)=\sum\limits_{d\mid n}\sigma(d)$ prime?

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