Displaying similar documents to “Sur la structure de la suite des diviseurs d'un entier”

Sur les entiers inférieurs à x ayant plus de log ( x ) diviseurs

Marc Deléglise, Jean-Louis Nicolas (1994)

Journal de théorie des nombres de Bordeaux

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Let τ ( n ) be the number of divisors of n ; let us define S λ ( x ) = C a r d n x ; τ ( n ) ( log x ) λ log 2 if λ 1 C a r d 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