Geodesic
On the Distribution of Square-Free Numbers
Canadian journal of mathematics, Tome 25 (1973) no. 6, pp. 1216-1223

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

Erdös [1] has shown that, if the square-free numbers in ascending order be denoted by s1, s2, ... , sn, ... , then for 0 ≦ γ ≦ 2 as x → ∞. In this paper we shall extend this result by proving that the asymptotic formula in fact holds for the wider range 0 ≦ γ ≦ 3.Similar results have been obtained previously by the author in respect of both the sequence of numbers expressible as the sum of two squares and also sequences of numbers relatively prime to given large integers, although the method used here differs from that of the earlier papers [2; 3]. 
Hooley, C. On the Distribution of Square-Free Numbers. Canadian journal of mathematics, Tome 25 (1973) no. 6, pp. 1216-1223. doi: 10.4153/CJM-1973-129-0
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