Geodesic
On the relative primality of $n$ and $f(n)$
Matematičeskie zametki, Tome 11 (1972) no. 3, pp. 259-268.

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We establish the asymptotic distribution of the set of natural numbers in the interval $[1, x]$ relatively prime to the corresponding value of an additive arithmetic function. The bibliography contains seven references. 
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     author = {A. S. Fainleib},
     title = {On the relative primality of $n$ and $f(n)$},
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     year = {1972},
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A. S. Fainleib. On the relative primality of $n$ and $f(n)$. Matematičeskie zametki, Tome 11 (1972) no. 3, pp. 259-268. http://geodesic.mathdoc.fr/item/MZM_1972_11_3_a3/