Scientia Magna, June 1st, 2006
Abstract In this paper we prove that 12 is the only Smarandache perfect number.
Keywords Smarandache function, Smarandache perfect number, divisor function.
[section]1. Introduction and result
Let N be the set of all positive integer. For any positive integer a, let S(a) denote the Smarandache function of a. Let n be a postivie integer. If n satisfy
[summation over (d|n)] S(d) = n + 1 + S(n), (1)
then n is called a Smarandache perfect number. Recently, Ashbacher [1] showed that if n [less than or equal to] [10.sup.6], then 12 is the only Smarandache perfect number. In this paper we comp...
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