## Applications of Smarandache Function, and Prime and Coprime Functions

**Authors:** Sebastián Martín Ruiz

The Smarandache function is defined as follows:
S(n)= the smallest positive integer such that S(n)! is divisible by n. [1]
In this article we are going to see that the value this function takes when n
is a perfect number of the form n = 2^{k - 1}.(2^{k} - 1) , p = 2^{k} - 1 being a prime
number.

**Comments:** 25 pages

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### Submission history

[v1] 7 Mar 2010

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