Let (the -th Jordan totient function, and for the Euler phi function), and consider the associated error term . When , both and are finite, and we are interested in estimating these quantities. We may consider instead since from [AS] and from the present paper . We show that belongs to an interval of the form , where as . From a more practical point of view we describe an algorithm capable of yielding arbitrary good approximations of . We apply this algorithm to the small values of and obtain and .
@article{JTNB_1991__3_2_311_0, author = {P\'etermann, Y.-F. S.}, title = {Oscillations d'un terme d'erreur li\'e \`a la fonction totient de {Jordan}}, journal = {S\'eminaire de th\'eorie des nombres de Bordeaux}, pages = {311--335}, publisher = {Universit\'e Bordeaux I}, volume = {2e s{\'e}rie, 3}, number = {2}, year = {1991}, mrnumber = {1149800}, zbl = {0749.11041}, language = {fr}, url = {http://www.numdam.org/item/JTNB_1991__3_2_311_0/} }
TY - JOUR AU - Pétermann, Y.-F. S. TI - Oscillations d'un terme d'erreur lié à la fonction totient de Jordan JO - Séminaire de théorie des nombres de Bordeaux PY - 1991 SP - 311 EP - 335 VL - 3 IS - 2 PB - Université Bordeaux I UR - http://www.numdam.org/item/JTNB_1991__3_2_311_0/ LA - fr ID - JTNB_1991__3_2_311_0 ER -
Pétermann, Y.-F. S. Oscillations d'un terme d'erreur lié à la fonction totient de Jordan. Séminaire de théorie des nombres de Bordeaux, Série 2, Tome 3 (1991) no. 2, pp. 311-335. http://www.numdam.org/item/JTNB_1991__3_2_311_0/
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