Main Article Content
This paper generalizes and improves the results of Margenstren, by proving that the number of -practical numbers which is defined by has a lower bound in terms of . This bound is more sharper than Mangenstern bound when Further general results are given for the existence of -practical numbers, by proving that the interval contains a -practical for all
Received 10/10/2019, Accepted 4/2/2020, Published 1/12/2020
This work is licensed under a Creative Commons Attribution 4.0 International License.
Margenstren. M. Les NombrsPractiques; Theorie, Observations et Conjectures. JNT, 37, 1991; 1-36.
Nicholas S, Lola Th.A Generalization of the Practical Numbers", IJNT, 14(05) 2018; 1487-1503.
Leonetti P, Sanna C.Practical Numbers Among the Binomial Coefficients.2019 (to appear).
Wang LY, Sun ZW. On practical numbers of some special forms. arXiv :1809.01532. 11 Jul 2019 .
Hausman M, Shapiro HN. On practical numbers. COMMUN PUR APPL MATH. 1984 Sep; 37(5):705-13.
Saias E.Entiersa^' diviseurs denses 1. JNT, 62 1997; 163-191.
Weingartner A.Practical Numbers and Distribution of Divisors.Q. J. Math, 66 2015; 743-758.
Robinson D. F.Egyptian Fraction Via Greek Number Theory", The New Zeal. Math. Magazine. 16 〖N_2〗^0 1979; 47-52.