Geodesic
Reciprocals of Certain Large Additive Functions
Canadian mathematical bulletin, Tome 24 (1981) no. 2, pp. 225-231

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Let β(n) = ∑p|nP and B(n) = ∑Pα ||nαP denote the sum of distinct prime divisors of n and the sum of all prime divisors of n respectively. Both β(n) and B(n) are additive functions which are in a certain sense large (the average order of B(n) is π2n/(6 log n), [1]). 
Koninck, J.-M. De; Erdös, P.; Ivić, A. Reciprocals of Certain Large Additive Functions. Canadian mathematical bulletin, Tome 24 (1981) no. 2, pp. 225-231. doi: 10.4153/CMB-1981-035-7
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     author = {Koninck, J.-M. De and Erd\"os, P. and Ivi\'c, A.},
     title = {Reciprocals of {Certain} {Large} {Additive} {Functions}},
     journal = {Canadian mathematical bulletin},
     pages = {225--231},
     year = {1981},
     volume = {24},
     number = {2},
     doi = {10.4153/CMB-1981-035-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-035-7/}
}
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