# Smarandache function

From Encyclopedia of Mathematics

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