J. M. De Koninck

Some randomly selected arithmetical sums

for some specific choices of j . In particular, for j = 1, or whenever j is preassigned, it is not difficult to show that R~(x)~cjx with a computable constant cj. On the other hand, when j=co(n), the problem of finding good approximations to Rj(x) becomes very difficult; by refining several earlier results, Ivi6 and Pomerance [5] found the best known approximation. Quite remarkably, the case of j = c o ( n ) 1 , or j=co(n ) -k with k fixed, shows no similarity to the case of j=co(n), and asymptotic expressions are in fact known (Erd6s and Ivi6 [3]):