# Smarandache function

From Encyclopedia of Mathematics

The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

Given a natural number $n$, the value of the Smarandache function $ \eta $ at $n$ is the smallest natural number $m$ such that $n$ divides $m!$. An elementary observation is that $\eta ( n ) \leq n$, and that $\eta ( n ) = n$ if and only if $n$ is a prime number or equal to $4$.

#### 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=50070

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