Polynomial analogue of the Smarandache function
نویسندگان
چکیده
منابع مشابه
Bounding the Smarandache Function
Let S (n), for n E N+ denote the Smarandache function, then S (n) is defined as the smallest m E N+, with nlm!. From the definition one can easily deduce that if n = prlp~2 .. . p~k is the canonical prime factorization of n, then Sen) = max{S(pfi)}, where the maximum is taken over the i's from 1 to k. This observation illustrates the importance of being able to calculate the Smarandache functio...
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The Pseudo-Smarandache Function is part of number theory. The function comes from the Smarandache Function. The Pseudo-Smarandache Function is represented by Z(n) where n represents any natural number. The value for a given Z(n) is the smallest integer such that 1+2+3+ . . . + Z(n) is divisible by n. Within the Pseudo-Smarandache Function, there are several formulas which make it easier to find...
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توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی
15 صفحه اولThe Average Smarandache Function
might hold (the authors of [6] claim that (4) has been tested by Ibstedt in the range x S 5 . 106 in [4J. Although I have read [4J carefully, I found no trace of the aforementioned computation!). In this note, we show that -I x is indeed the correct order of magnitude of ogx A(x). For any positive real number x let 7I"(x) be the number of prime numbers less then or equal to x, B(x) = xA(x) = 2:...
متن کاملOn the Pseudo-Smarandache Function
Kashihara[2] defined the Pseudo-Smarandache function Z by m(m+l) } Properties of this function have been studied in [1], [2] etc. 1. By answering a question by C. Ashbacher, Maohua Le proved that S(Z(n»-Z(S(n» changes signs infmitely often. Put d s,z (n) = I S(Z(n»-Z(S(s» I We will prove first that lim inf d s,z (n) ~ 1 (1) n-oo and (2) n-+oo p(p+l) Indeed, let n = , where p is an odd prime. Th...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2020
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2020.05.015