Smarandache function

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