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

Voir la notice de l'article provenant de la source Cambridge University Press

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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