Given an integer base and a completely -additive arithmetic function taking integer values, we deduce an asymptotic expression for the counting function
under a mild restriction on the values of . When , the base sum of digits function, the integers counted by are the so-called base Niven numbers, and our result provides a generalization of the asymptotic known in that case.
Étant donnés un entier naturel et une fonction complètement q-additive à valeurs dans l’ensemble des nombres entiers relatifs, on calcule une expression asymptotique de la fonction qui à associe la cardinalité de l’ensemble
quand les valeurs de sont soumises à une petite restriction. Dans le cas où , la somme des chiffres d’un nombre en base , les valeurs de la function comptent les nombres q-Harshad. Donc, notre résultat généralise la formule asymptotique dans ce cas.
@article{JTNB_2009__21_3_503_0, author = {Daileda, Ryan and Jou, Jessica and Lemke-Oliver, Robert and Rossolimo, Elizabeth and Trevi\~no, Enrique}, title = {On the counting function for the generalized Niven numbers}, journal = {Journal de th\'eorie des nombres de Bordeaux}, publisher = {Universit\'e Bordeaux 1}, volume = {21}, number = {3}, year = {2009}, pages = {503-515}, doi = {10.5802/jtnb.685}, mrnumber = {2605530}, zbl = {1205.11105}, language = {en}, url = {http://www.numdam.org/item/JTNB_2009__21_3_503_0} }
Daileda, Ryan; Jou, Jessica; Lemke-Oliver, Robert; Rossolimo, Elizabeth; Treviño, Enrique. On the counting function for the generalized Niven numbers. Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 3, pp. 503-515. doi : 10.5802/jtnb.685. http://www.numdam.org/item/JTNB_2009__21_3_503_0/
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