Abstract
AbstractAn 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.
Publisher
Springer Science and Business Media LLC
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