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On the [kappa]-power, free number sequence.
- Article from:
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Smarandache Notions Journal
- Article date:
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January 1, 2004
- Author:
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Copyright informationCOPYRIGHT 2004 American Research Press. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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Abstract. The main purpose of this paper is to study the distribution properties of k-power free numbers, and give an interesting asymptotic formula.
Key words and phrases. k-power free numbers; Mean Value; Asymptotic formula.
1. INTRODUCTION AND RESULTS
A natural number n is called a k-power free number if it can not be divided by any [p.sup.k], where p is a-prime number. One can obtain all k-power free number by the following method: From the set of natural numbers (except 0 and 1)
-take off all multiples of [2.sup.k](i.e. [2.sup.k], [2.sup.k+1], [2.sup.k+2] ...).
-take off all multiples Of [3.sup.k].
-take off all multiples of [5.sup.k].
... ...