Geodesic
Asymptotic Formulas for Some Arithmetic Functions
Canadian mathematical bulletin, Tome 1 (1958) no. 3, pp. 149-153

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Let f(x) be an increasing function. Recently there have been several papers which proved that under fairly general conditions on f(x) the density of integers n for which (n, f(n)) = 1 is 6/π2 and that (d(n) denotes the number of divisors of n) In particular both of these results hold if f(x) = xα, 0 < α < 1 and the first holds if f(x) = [α x], α irrational. 
Erdős, P. Asymptotic Formulas for Some Arithmetic Functions. Canadian mathematical bulletin, Tome 1 (1958) no. 3, pp. 149-153. doi: 10.4153/CMB-1958-014-1
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     title = {Asymptotic {Formulas} for {Some} {Arithmetic} {Functions}},
     journal = {Canadian mathematical bulletin},
     pages = {149--153},
     year = {1958},
     volume = {1},
     number = {3},
     doi = {10.4153/CMB-1958-014-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1958-014-1/}
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