Difference between revisions of "Smarandache function"
From Encyclopedia of Mathematics
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| + | 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 $4$. | ||
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| − | <table>< | + | <table><tr><td valign="top">[a1]</td> <td valign="top"> F. Smarandache, "A function in number theory" ''Smarandache Function J.'' , '''1''' (1990) pp. 3–65</td></tr></table> |
Latest revision as of 16:55, 1 July 2020
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=14174
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