Sur les entiers inférieurs à x ayant plus de log(x) diviseurs
Journal de Théorie des Nombres de Bordeaux, Volume 6 (1994) no. 2, pp. 327-357.

Let τ ( n ) be the number of divisors of n ; let us define S λ ( x ) = Card n x ; τ ( n ) ( log x ) λ log 2 if λ 1 Card n x ; τ ( n ) < ( log x ) λ log 2 if λ < 1 It has been shown that, if we set f ( λ , x ) = x ( log x ) λ log λ - λ + 1 log log x the quotient S λ ( x ) / f ( λ , x ) is bounded for λ fixed. The aim of this paper is to give an explicit value for the inferior and superior limits of this quotient when λ 2 . For instance, when λ = 1 / log 2 , we prove lim inf S λ ( x ) f ( λ , x ) = 0 . 938278681143 and lim inf S λ ( x ) f ( λ , x ) = 1 . 148126773469

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     author = {Marc Del\'eglise and Jean-Louis Nicolas},
     title = {Sur les entiers inf\'erieurs \`a $x$ ayant plus de $\log (x)$ diviseurs},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
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     publisher = {Universit\'e Bordeaux I},
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     year = {1994},
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Marc Deléglise; Jean-Louis Nicolas. Sur les entiers inférieurs à $x$ ayant plus de $\log (x)$ diviseurs. Journal de Théorie des Nombres de Bordeaux, Volume 6 (1994) no. 2, pp. 327-357. doi : 10.5802/jtnb.118. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.118/

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