Geodesic
An Asymptotic Formula for Reciprocals of Logarithms of Certain Multiplicative Functions
Canadian mathematical bulletin, Tome 21 (1978) no. 4, pp. 409-413

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Sums of the form where f(n) is a multiplicative arithmetical function and denotes summation over those values of n for which f(n)>0 and f(n) ≠1, were studied by De Koninck [2], De Koninck and Galambos [3], Brinitzer [1] and Ivič [5]. The aim of this note is to give an asymptotic formula for a certain class of multiplicative, positive, primeindependent functions (an arithmetical function is prime-independent if f(pv) = g(v) for all primes p and v = 1, 2, ...). This class of functions includes, among others, the functions a(n) and τ(e)(n), which represent the number of nonisomorphic abelian groups of order n and the number of exponential divisors of n respectively, and none of the estimates of the above-mentioned papers may be applied to this class of functions. We prove the following. 
Koninck, Jean-Marie de; Ivić, Aleksandar. An Asymptotic Formula for Reciprocals of Logarithms of Certain Multiplicative Functions. Canadian mathematical bulletin, Tome 21 (1978) no. 4, pp. 409-413. doi: 10.4153/CMB-1978-072-4
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     author = {Koninck, Jean-Marie de and Ivi\'c, Aleksandar},
     title = {An {Asymptotic} {Formula} for {Reciprocals} of {Logarithms} of {Certain} {Multiplicative} {Functions}},
     journal = {Canadian mathematical bulletin},
     pages = {409--413},
     year = {1978},
     volume = {21},
     number = {4},
     doi = {10.4153/CMB-1978-072-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1978-072-4/}
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