# Smarandache function

From Encyclopedia of Mathematics

Given a natural number , the value of the Smarandache function at is the smallest natural number such that divides . An elementary observation is that , and that if and only if is a prime number or equal to .

#### References

[a1] | F. Smarandache, "A function in number theory" Smarandache Function J. , 1 (1990) pp. 3–65 |

**How to Cite This Entry:**

Smarandache function.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Smarandache_function&oldid=14174

This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article