# Smarandache function

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## Smarandache function

[‚smär·ən′dä·chē ‚fənk·shən]
(mathematics)
A function η defined on the integers with the property that η(n) is the smallest integer m such that m ! is divisible by n.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Ashbacher, An introduction to the Smarandache function, Erhus Univ.
The pseudo Smarandache function, Z(n), introduced by Kashihara [1], is as follows:
For any positive integer n, the Smarandache function S(n) can be defined as follows: S(n) is the smallest number, such that S(n)!
This paper as a note of Gou Su's work, we consider the hybrid mean value properties of the Smarandache kn-digital sequence and Smarandache function S(n), which is defined as the smallest positive integer m such that n|m!.
[5] Du Fengying, On a conjecture of the Smarandache function S(n), 23(2007), No.
The pseudo Smarandache function, denoted by Z(n), has been introduced by Kashihara [1].
[1] Wenpeng Zhang and Ling Li, Two problems related to the Smarandache function, Scientia Magna, Vol.
[10] Charles Ashbacher, Some problems on Smarandache function, Smarandache Notions Journal, Vol.
one obtains the Smarandache function S(n), and its dual S*(n), given by
[3] F.Mark, NLPatrick, Bounding the Smarandache function, Smarandache Notions Journal, 13(2002), 37-42.
Now we let S(n) be the Smarandache function. That is, S(n) denotes the smallest positive integer m such that n divide m!, or S(n) = min{m : n | m!}.
For any positive integer n, the famous Smarandache function S(n) is defined as the smallest positive integer m such that n | m!.
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