The Distribution of Squarefull Numbers in Short Intervals

نویسندگان

  • Michael Filaseta
  • Ognian Trifonov
چکیده

It follows that there is a positive constant c1 and arbitrarily large values of x for which the interval (x; x+ c1x ] contains no squarefull numbers. On the other hand, since there is a square in (x; x + 2 p x + 1] for all x 0, it follows that there is a constant c2 such that for every x 1, the interval (x; x + c2x] contains a squarefull number. Thus, the order of the maximum size of gaps between squarefull numbers is known. However, a better understanding of the distribution of squarefull numbers in short intervals can still be obtained. The result of Bateman and Grosswald easily implies that

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Order intervals in the metric space of fuzzy numbers

In this paper, we introduce a function in order to measure the distancebetween two order intervals of fuzzy numbers, and show that this function isa metric. We investigate some properties of this metric, and finally presentan application. We think that this study could provide a more generalframework for researchers studying on interval analysis, fuzzy analysis andfuzzy decision making.

متن کامل

Detecting squarefree numbers

We present an algorithm, based on the explicit formula for L-functions and conditional on GRH, for proving that a given integer is squarefree with little or no knowledge of its factorization. We analyze the algorithm both theoretically and practically, and use it to prove that several RSA challenge numbers are not squarefull.

متن کامل

Another Method for Defuzzification Based on Regular Weighted ‎Point‎

‎A new method for the defuzzification of fuzzy numbers is developed in this paper. It is well-known, defuzzification methods allow us to find aggregative crisp numbers or crisp set for fuzzy numbers. But different fuzzy numbers are often converted into one crisp number. In this case the loss of essential information is possible. It may result in inadequate final conclusions, for example, expert...

متن کامل

Determining the most appropriate probability distribution function for calculate and compare the SPEI and SPI drought index in Tehran

Introduction: The study of drought as a natural phenomenon that affects the lives of most people is very important. According to researchers in the field of drought, rainfall, temperature, evaporation, wind and relative humidity have been shown to play an important role in drought. The low variety of data required and the simplicity of calculating the SPI index led to its widespread use. The ef...

متن کامل

Exact maximum coverage probabilities of confidence intervals with increasing bounds for Poisson distribution mean

 ‎A Poisson distribution is well used as a standard model for analyzing count data‎. ‎So the Poisson distribution parameter estimation is widely applied in practice‎. ‎Providing accurate confidence intervals for the discrete distribution parameters is very difficult‎. ‎So far‎, ‎many asymptotic confidence intervals for the mean of Poisson distribution is provided‎. ‎It is known that the coverag...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1994