Sur les entiers inférieurs à x ayant plus de log(x) diviseurs
Journal de Théorie des Nombres de Bordeaux, Tome 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

@article{JTNB_1994__6_2_327_0,
     author = {Del\'eglise, Marc and Nicolas, Jean-Louis},
     title = {Sur les entiers inf\'erieurs \`a $x$ ayant plus de $\log (x)$ diviseurs},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {327--357},
     publisher = {Universit\'e Bordeaux I},
     volume = {6},
     number = {2},
     year = {1994},
     zbl = {0839.11041},
     mrnumber = {1360649},
     language = {fr},
     url = {www.numdam.org/item/JTNB_1994__6_2_327_0/}
}
Deléglise, Marc; Nicolas, Jean-Louis. Sur les entiers inférieurs à $x$ ayant plus de $\log (x)$ diviseurs. Journal de Théorie des Nombres de Bordeaux, Tome 6 (1994) no. 2, pp. 327-357. http://www.numdam.org/item/JTNB_1994__6_2_327_0/

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