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- W2312321405 abstract "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(p v ) = 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." @default.
- W2312321405 created "2016-06-24" @default.
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- W2312321405 date "1978-12-01" @default.
- W2312321405 modified "2023-10-14" @default.
- W2312321405 title "An Asymptotic Formula for Reciprocals of Logarithms of Certain Multiplicative Functions" @default.
- W2312321405 doi "https://doi.org/10.4153/cmb-1978-072-4" @default.
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