On some classes of multiplicative functions

An arithmetical function f is multiplicative if $$f(1)=1$$ f ( 1 ) = 1 and $$f(mn)=f(m)f(n)$$ f ( m n ) = f ( m ) f ( n ) whenever m and n are coprime. We study connections between certain subclasses of multiplicative functions, such as strongly multiplicative functions, over-multiplicative functions and totients. It appears, among others, that the over-multiplicative functions are exactly same as the totients and the strongly multiplicative functions are exactly same as the so-called level totients. All these functions satisfy nice arithmetical identities which are recursive in character.