Sur un problème d'optimisation en nombres entiers de T.L. Saaty
Ordre maximal d’un élément du groupe des permutations et «highly composite numbers»
On partitions without small parts
Let denote the number of partitions of into parts, each of which is at least . By applying the saddle point method to the generating series, an asymptotic estimate is given for , which holds for , and .
Sur une application de la formule de Selberg-Delange
E. Landau has given an asymptotic estimate for the number of integers up to x whose prime factors all belong to some arithmetic progressions. In this paper, by using the Selberg-Delange formula, we evaluate the number of elements of somewhat more complicated sets. For instance, if ω(m) (resp. Ω(m)) denotes the number of prime factors of m without multiplicity (resp. with multiplicity), we give an asymptotic estimate as x → ∞ of the number of integers m satisfying , all prime factors of m are congruent...
Statistiques sur
On practical partitions.
Sommes de sous-ensembles
Even partition functions.
Page 1