The following corollary demonstrates that in order to calculate the value $\beta(n)$ of a multiplicative function $\beta:\mathbb N\to\mathbb C$ it is sufficient to know the values of $\beta(p^e)$ on all maximal powers of prime numbers $p^e$ with $p^e\mid n.$# Corollary: Simple Conclusions For Multiplicative Functions
(related to Definition: Multiplicative Functions)
For all multiplicative functions $\beta:\mathbb N\to\mathbb C$ we have $\beta(1)=1$ and $$\beta(n)=\prod_{i=1}^\infty{\beta(p_i^{e_i})}$$ for the factorization of $n=\prod_{i=1}^\infty p_i^{e_i}.$
Proofs: 1
Examples: 1
