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Article: A lower bound for S ([2.sup.p-1]([2.sup.p]-1)).(Brief article)
- Article from:
- Smarandache Notions Journal
- Article date:
- January 1, 2001
- Author:
CopyrightCOPYRIGHT 2001 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. Let p be a prime, and let n = [2.sup.p-1]([2.sup.p]-1).In this paper we prove that S(n) [greater than or equal to] 2p+1.
Key words. Smarandache function, function value, lower bound.
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For any positive integer a, Iet S(a) be the Smarandache function. In[2], Sandor showed that if (1) 11 = [2.sup.p-1]([2.sup.p]-1) is an even
perfect number, then S(n) = [2.sup.p]-1. It is a well known fact that if n is an even perfect number then p must be a prime. But, its inverse proposition is false (see [1, Theoemzs 18 and 276]). In this paper we give a lower bound for S(n) in the general cases. We prove the following result.
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