Ramanujan Expansions of Certain Arithmetic Functions

We consider two arithmetic functions f and f’ which are related by the equation (0.1) f ( i ) = ∑ j | i f' ( j ) ,       ( i = 1 , 2 , 3 , … ) . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315139463/240bbb93-6815-40d4-a336-935ccad8ea72/content/eq1979.tif"/>